I'm sure they could do an entire vegetarian tasting menu, but you could call and ask to be sure.
As for a la carte, you would have to stick with antipasti and pastas but we once did an entire meal out of antipasti and half portions of pastas and it was wonderful. Some contenders among the standard menu would be:
Sweet onion crepe
And based on the current menu listed on the website:
Artichoke salad with arugula and parmesan
Asparagus flan with raw asparagus salad
Eggplant canneloni with heirloom tomatoes
Fettuccine with corn and charred scallion
Escarole ravioli with toasted pine nuts and honey
So, I definitely think it can be done and I think it would be worth it. I find their pastas to be very interesting and would definitely do a night of half portions again.