By bank I’m assuming the poke bank app on the 3Ds. The question kinda has 2 answers.
If the Haxours is poorly hacked, it won’t be allowed in the poke bank.
If it’s hacked correctly, but still level 1, it might be allowed through, and the poke bank would do nothing about it.
Source: Having a level 1 Aegislash in the poke bank.