I left my luggage there behind/beside the desk for about 6 hours once. No worries, they keep something of an eye on it. I have never once had a problem with leaving luggage in a Metropolitan Lounge/ClubAcela in the unattended baggage storage at LA, New York, Washington, DC and Chicago (pre-Red Cap era, haven't been there since the new lounge opened). Frankly, I found the Red Cap thing in Chicago kind of a pain and am just as glad it is gone.
Personally, I like using the tunnel and the boarding ramp in LA. Since the first time I was ever in the station was in 1958 when I was three, the tunnel and ramp just feel like Union Station ought to. I go so far as to use the steeper left side ramps, since they are original. The less steep, handicapped friendly ramps with the stairs in the middle on the right were put in when they closed the tunnel and did some rebuilding for a couple years when they put the Red Line subway in during the 80s