I guess I should weigh in in more detail since I just did this same trip, pretty much, only from Tucson. As far as the baggage goes, it getting in later isn't a big deal as long as you don't mind going back to the station for it. If you're planning on going straight from the train station to the park, you don't want to have to deal with your bags anyway. If it works better for you to drop them off at the hotel first, then just check them to LAX and pick them up there, carrying them on to the Surfliner. Either way, you're going to be making a detour, whether to your hotel in the morning or to the train station later in the day.
In our case, my brother was driving down overnight to meet us, and was planning to leave his car at the hotel anyway, so we planned to pick up our bags in LAX and take the with us on the train to Anaheim. It's good that we did, because my brother ended up getting into the LA area much earlier than planned, and he just picked us up at Union Station (We got in about 5:15am, incidentally, and he was there by 6:00, so we got to Anaheim about the same time that first Surfliner would have). We drove to the hotel, left our bags in the car, then took the ART shuttle from our hotel to the park. We spent a few days at the park, using the ART shuttle everyday, and it worked out great. The ART drivers were always very cheerful and helpful and friendly.
On the last day, my brother was leaving 5:00am in the morning, and we were planning on spending another day at the park, so we had to figure out how to handle the trip back. We could have checked out of the hotel, in the morning and left our bags there, but then when we left Disneyland, we'd have to take the ART back to the hotel for the bags, then take it back to Disneyland (because that's nearly the only transfer point between all the routes), then take it to the train station. Or, I thought we would be better off by just all heading out to Disneyland in the morning with the luggage, sending my wife and kids into the park, then having me ride the ART out to the train station to check the bags all the way to Tucson. Then, no longer encumbered by baggage, I could shuttle back to Disneyland, spending the rest of the day there, then all ride to the train station in the evening.
This was a great plan, except for the fact that the Anaheim station was CLOSED when we got there. There's a sign by the door that says "closed at various times for meal breaks", so it's not just an emergency schedule snafu. That really angered me, because I had to wait a half hour in the middle of the day for them to reopen, which because of the ART scheduling and the frequencies of the shuttles caused me to get back to Disneyland about an hour later than I would have. Let me state clearly and unequivocally that I don't begrudge anyone their mealtime. And, I understand the operational realities of Amtrak staffing means that they can't have two people at every station at every time. That's not the issue. The issue for me is that having never been to the Anaheim station before and never having planned a Disneyland trip dependent upon Amtrak before, I did a lot of research before hand to make sure our plan would work. And, part of that was making sure I'd be able to get to the station to check our bags in the middle of our last day. I checked online for the Anaheim station hours, and confirmed them with a phone rep. Not once did anyone tell me "Oh, they're also closed at random times". Had I known that I would have left the bags at the hotel and shuttle around later, or just sprung for a taxi to get them at the end of the day. Again, the issue is not suggesting that employees shouldn't get time off. It's just an issue of not following through with a written commitment to customers. If the reality of the staffing situation is such that they can't meet the hours they specify on their site and in the other printed materials, no problem. Just print different hours that allow for the employee breaks as necessary. If those can't be nailed down to specific times because the train timekeeping isn't good enough, again, no problem. Just have a way of notating in the schedule that the station is closed sometimes during the listed hours when the trains aren't there.
Anyway, sorry for the ranty detour, but I felt the need to warn you about Anaheim station scheduling in case you're dependent on the staff actually being there. That, and losing an hour with my family at Disneyland marred what was otherwise a good Amtrak experience.
When we were done at the park the last day, we took the ART to the station and actually got dropped off at a city bus stop about a half mile away. This driver was the opposite in attitude to all the other ART drivers, and was arguing with some other passengers at the start of the trip. I questioned the driver if this was really the stop for the station and he insisted it was, despite me having taken the ART there just that morning. I didn't press it further, because I was on a different number than I was in the morning, and thought maybe I wasn't as familiar with the route as I thought I was. But, by the time we walked to the station I was on the phone with an ART dispatcher, and he assured me I was right, and they had no idea what that guy was thinking. They took the problem very seriously, and called me again the next day to talk about the retraining they were doing for the driver and offering to refund our whole family's passes for the week. I told them that wasn't necessary; that just taking us seriously was the only thing necessary to make us feel better. That's in marked contrast to Amtrak, which blew me off when I called about the Anaheim station, first saying that I was wrong, that the station didn't close, (because how could it when the hours on the agent's screen said it didn't?), then finally agreeing to write it up and pass it along but specifically telling me not to expect any changes.
Sorry, ranting again. Anyway, just wanted to let you know that a train trip to Disneyland can be done, and the ART is indeed useful and works reliably as long as you don't get the driver who clearly had something else going on his head that day. The one thing I might try next time is to book a hotel that's on ART route 14 or 15 (the two routes that go to the train station), so that I can get between the station and the hotel without transferring at Disneyland. Or picking a hotel that's on a route that intersects with 14 or 15 somewhere closer. Either that or just suck it up and pay for a taxi for that last day. I just get really cheap about everything else on a Disneyland trip so that I can justify staying longer at the park and buying more food and souvenirs and everything.