Yes, I transported our children's bike on it without any additional fastening. It is a LIKEaBIKE LIKEtoBIKE (20") or the 20" children's bike from Ghost.

Yes, that should fit.
We have even transported the very small ones and even the wheels with it. If the wheel distance was too small, we tied the wheel to the carrier with a shortened tension strap.
But this should no longer be necessary for 20 inch wheels.