IIRC, as far as the US was concerned, the purpose of the draft, post pearl harbor, was not so much to conscript as it was to control the huge influx of young men that wanted to join up.
The draft existed to feed the needs of the army. The other services filled on their own. Enlisting in the Navy or Marines was not difficult to do. There were always ways to avoid military service as well; examine the Romney family history for various methods.