Yes it is possible to swallow without the use of your tongue.
You just need to push the food further back to your throat and then use your throat to suck the food down your throat by doing your normal gulping or swallowing motion.
I tried swallowing without the use of my tongue and I was able to swallow the food without needing my tongue.
So if a person were to not have a tongue then they could still swallow without it.
Also it's a myth that someone could swallow their tongue during a seizure but that is impossible because the tongue is securely attached and would not be able to be swallowed.