Quick answer:
Yes.
<Added>Long answer:
You can't upload the same piece of work in more than one grou at the same time. You will either have to wait two days and upload another copy of the work in the second group, or stick a link to the story in the Topics section of the second group.
You can join as many groups as you like (depending on whether or not there's space), but it will mean extra critting commitments.