I'll be the voice of the opposition here... When we went, the party we were seated with had a little one, and the waitress recommended seating him at the corner of the table. From that position, a baby/toddler would have to be standing in his high chair to reach the cooking surface. And a 2 month old isn't going to be mobile enough to pose a problem at all. True, there isn't much room for an infant carrier, but that's true at just about every Disney restaurant we've been to because of the way they pack the tables in!
We haven't taken DD8mo to Disney yet, but she's been to a Teppan Edo type restaurant in the real world without difficulty. If you want to try it, I'd say go for it.