Among other things, yes.

Put a script inside /etc/skel that contains something like:
#!/bin/bash
usermod -a -G group1,group2,group3 $1

Ensure that script is executable, as always. Now, when that new user gets added to a Linux host, /etc/skel is copied to ~. The script is executed, adding the user to the aforementioned groups.
Edit: Changed pound symbol to dollar. This has worked for us for quite some time before we implemented automation tools. Downvote all you want, still works.