Yes, it can.
You need to find a Pokemon that likes playing with your Noibat to get eggs easily.
Two Pokemon not of the same egg group will ignore each other.
Two Pokemon of the same egg group, same species, or a Pokemon and a Ditto that all have the same trainer ID will not like each other very much.
A Pokemon and a Ditto or two Pokemon of the same egg group with different trainer ID's will get along okay.
Two Pokemon of the same species (I.E. Eevee) with different trainer ID's will get along fantastically.
Even if they don't like each other very much you'll still get eggs, it just takes longer. If it says "they prefer to play with other Pokemon", you won't get eggs at all because
1. They are incompatible (not of the same egg group)
2. They are the same gender
3. One of them is in the Undiscovered egg group.
So maybe double-check if your Noibat is the same gender as your Fearow/Trapinch.
Here is a guide to breeding in XY.