It still might. They do bend their bodies and tails. I know several people who keep them in 10 gallon tanks, but really after 2 years that's just asking for trouble.
On an axolotl forum I recently asked to see pictures of axolotls in their tanks and for people to tell me the size of them.
So for instance. This is a HALF grown axolotl in a half size tank. A 5 inch animal in a 10 gallon
You can't see the whole animal, but you can see how their is about as much room as we would give our bettas to swim in a 5 gallon. If that axolotl was 10 inches you can imagine it would get a little cramped--but in a tank twice as big, a 20 gallon, it would be about exactly the same dimensions! And a 15 gallon would even still be a decent amount of space.
You could honestly start out the baby in the 10 gallon if you wanted, you can see how tiny they are (and this isn't even an itty bitty baby size)