My first instinct would be to say no - I know my family would not, but we're not speed eaters. Generally, allot about 90 minutes for a sit down meal. Don't forget that this one has characters, so if you speed through your meal, you might miss some of them. The only thing working for you is that Garden Grill is a fixed menu place (i.e., you don't order per se, so the food can come quicker). After you're meal you will have to get to WS and find a place to stand. Depending on when you're there, that might be easy or it might be hard to find a place with a good view. Luckily, there are a lot of places around WS lagoon with good views.
I'd say you should either decided to have dinner at GG and if things work out, go see IllumiNations OR see IllumiNations and find somewhere else to eat. I would not want to spend the entire meal watching the clock.