When I've flown I've never been asked the size of my bag. Most of the time they don't even know a dog is in it
I think as long as it will fit under the seat it wont be an issue. One time I flew the atttendents let me sit Mitzy on my lap, but I think it was only because the flight was pretty empty and the attendents wanted to see her.
If its a soft sided bag though I'm sure it will be ok because it will be able to mold a little under the seat where as a hard sided crate/kennel would not be able to.