Context is definitely possible.
I'm not sure that I actually intentionally taught Tamber this, but, I do talk to him in context all the time and he does know some things in context.
He will only say, "Good morning" first thing in the morning.
When he smells cooking he says, "Good stuff." I originally only taught him "Good stuff" as what I say when I give him a special treat and only in the morning. He has generalized this to all food and any time of day.
He now says, "Hey! Cut that out!" to ~all~ loud obnoxious sounds. It started as his imitation of my husband yelling at Teyla's screaming.
When he's on his swing, he'll say, "I'm a swinger!" or "I like to swing" and also "Weeeee." I taught him these. Now all I have to do is say one of those things and he will get on his swing and start swinging.
He invites me to pet him by saying, "Mommy pet." (He doesn't always like to be pet, so this was a bit of a breakthrough of understanding on his part of our training sessions.)
He will ask to come out of his cage by saying, "Wanna come out?"
I can ask him if he wants a nut and he will shake his head up and down. Conversely, if he wants a nut and I am not offering one to him, he will still shake his head up and down.
If he drops something on the bottom of the cage that he wants me to pick up, he will say, "Help me." (This one was a misunderstanding. I was trying to get him to say "Pick up, please." But, I used "help me," many times in a different context when he flew somewhere and needed help at which time I'd pick him up. He is the one who generalized it.)
These are just a few of the things I can think of off the top of my head. I could easily list another set of things that we are working on trying to learn in context and haven't quite made it yet.