There is a lot of ambient noise at the Blue Bayou, so your kids laughing & singing isn't going to bother anybody. In my book, the sort of behavior that requires removing the child from the restaurant is crying, screaming, and having a temper tantrum.
In my experience, each successive day we are at DL, we start the day a little more tired than we were the day before. So maybe do a BB lunch on your first day...when your 3 yr old is pretty well rested and fresh.
I once was at Roy's Kahana Grill in Hawaii (Maui) and saw a family of 4 who had 2 younger children. The parents brought their kids to this fancy restaurant dressed in their pajamas and the kids spent the whole dinner with their noses in their iPad screens.
**For my family **, and your mileage may vary, it is just not worth it to spend almost $200 on lunch or dinner only to have 1 or both of my kids looking at a tablet or smart phone the entire time. We can do that any day of the week at home if we wanted to. Disneyland is for interacting on a person-to-person basis with your family and friends, and if my child couldn't handle sitting quietly for 15 minutes coloring or playing a quiet game with Mom or Dad until the food arrived, then we would do a Counter Service place instead...and we'd do Blue Bayou or a similar sit down restaurant another time when the child was older.
*** Edited to add ***
The above statements are not meant to be a judgement against anyone here who might make such choices. It really is an individual thing. You can still have a lovely and magical time at Disneyland without a meal at the Blue Bayou.