Probably, depends on the definition of full size. I have a large bag (much larger than airline carry on size) that I have taken on both the Adirondack and Maple Leaf with no problems, as well as the Cascades and Northeast Regionals. I almost never check bags on Amtrak. As far as large suitcases go, it is kind of middling. My daughter has a huge suitcase, and I mean huge, that she used to bring stuff back after living in Korea, that might be problematic. A normally "large" suitcase should be okay.
If you are northbound boarding at New York Penn Station, get a Red Cap. They'll not only get you down to track level before the crowd hits, they'll stow your suitcase for you.
One word of warning, I notice from other postings that you are planning to take the Canadian, and I assume that is part of this three week trip. Room for bags in roomettes and double bedrooms on board the Canadian is pretty small and there is no common storage like on Superliners, nor a big "cubby" in the room like on Viewliners. I made the mistake of taking the above-mentioned suitcase onboard and it took up pretty much all the floor space in my roomette. The attendant took pity on me and found a place to put it elsewhere in the car. Don't try to take a largish suitcase as a carry on on the the Canadian. Now I use my little gym bag to carry what I need enroute, which fits nicely on little shelf above the toilet, and check the big one.
Also, if you are taking one of the VIA corridor services between Montreal and Toronto, note that, unlike Amtrak, VIA does strictly enforce its carry on size and weight limits, at least at major stations, with scales and bag sizers. Business Class passengers have a bigger carry on allowance and only one train has checked baggage service (65, leaves Montreal at 11:00 am). Go to viarail.ca and look at their carry on bag limits, which are smaller than Amtrak's published limits, and decide if you need to go Business Class to get your bags on, or take the one train that has checked baggage.