Hi.
Yes - users can use any type of email account (Gmail, Yahoo, etc.), but that same account must be registered as a Microsoft profile. If they have a live.com, outlook.com, or hotmail.com account, then they already have this profile established.
Note that these people must log into their Live ID profile settings and ALLOW your account to send them group requests. Microsoft did all of this so that everyone wouldn't receive a bunch of random requests from strangers selling stuff.
I think the following Question/Answer will be helpful to you:
http://answers.microsoft.com/en-us/skydrive/forum/sdfiles-sdsharing/sending-skydrive-group-invites/dd64eb58-1d51-43bf-9fa2-0e7756b98473
Here is another one. Note that there are other helpful Q&As on the right side of the web page:
http://answers.microsoft.com/en-us/skydrive/forum/sdoptions-sdpeople/problem-with-invitations-to-join-group/53490e83-243f-4ce6-9a76-d9fcaa2bd539
Good luck!
Best wishes, Davin Mickelson
