SYR to NYP is probably my most frequent Amtrak corridor. There is ALWAYS, even if the train is late a smoke stop in Albany-Rensselaer. The crew always changes there and there are a ton of people who board the train to go down to New York. One or two of the coaches at the front of the train are even kept closed until Albany for the number of people boarding there. A standard SYR to NYP ride for me (have never upgraded to Business Class, although after trying the comfy seats at National Train Day I might have to) on a crowded day is two seats to myself from SYR to ALB and then getting a aisle seat mate for the 2 1/2 trip down the Hudson.
Train #280 until one of the recent timetable changes operated about an hour later (my grandmother, the reason I go to SYR missed it used to the old schedule) but today Arrives in Albany at 9:50am and Departs at 10:05am. Smoking is amazingly still permitted on the platforms in Albany, although last year (I believe) it was banned from LIRR and Metro-North platforms (within New York State).
I know on the LSL SYR is a smoke stop but when I board Empire Service trains I rarely see people stepping off to smoke. It would probably be one of those stops that if you ask the crew they might quickly let you smoke but don't announce it. Utica has never been a smoke stop in all my years riding the train, I have never stepped off the train there although on my next trip to Syracuse when I can I am definitely going to plan a layover to explore its historic station. (I've got every Empire Service station on my website except Utica, Amsterdam and Schenectady).