Can I plug a multi-outlet adapter into a GFCI outlet?
You can absolutely plug in an extension cord to the GFCI outlet, and as long as the GFCI outlet was wired correctly, the GFCI protection extends to all the devices plugged into it.

However, I would advise you to stay away from this kind of multi outlet adapter, since it might cover the GFCI buttons making it harder to test and reset: