Yes, but it will likely cost more than starting with a bicycle. Mounting an engine will require fabrication in all but a few cases.
I had considered making a motoped based on a modified moped frame.
The experts on that subject would be on mopedarmy.com
Looked around on their site and still couldn't find any definitive answers. Some say that an old moped with pedals qualifies as a motorized bike while oters say no. Just wanna make sure its legal otherwise ill just build a normal bike.
One thing you can do is take an old moped frame, cut off the part of the frame with the vin stamped into it, and weld it into whatever bicycle frame you want to use. Then you can register as a moped.