Is that an actual possibility?
Yes. It absolutely is a possibility and something that should be explored. The power of this action is more symbolic than actual--and the symbolic gesture towards prioritizing rail travel is important enough to support this effort.
While perhaps impractical for LD travel around the country, just the existence of an "Amtrak One" sends a positive message about passenger rail travel, even if Biden never uses it.
If Biden is to take the NEC to go from DC to Boston, or DC to Delaware, just bringing in the Secret Service to make NEC facilities more secure is a huge win for rail travel. Just like in airports, they put in HiDef cameras for terrorists but they use them afterwards to catch regular thieves.
It could work outside the NEC as well. Even if Biden were flown into Detroit and took "Amtrak One" from there to Chicago, the spectacle alone is worth the added costs of security. Imagine if they were able to rehabilitate buildings with sidings on them and use them for "Whistlestop" events.
Imagine if MSM was showing pictures of how beautiful the CZ route between Denver and SLC is!
As far as security goes, despite what events at the Capitol lead you to believe, most Presidential security is threat intelligence based and is very good. They know who has the capacity to make threats on the president and can usually address those threats long before people with weapons get close to POTUS or whatever vehicle they're traveling on.
There are a ton of ways to make this work. I hope the Biden administration acts on it.