Yes, it will run Final Cut Express fantastically with that configuration. The render times will never be as impressive as those of a MBP, but nonetheless it will be speedy and responsive.
GarageBand, even during heavy use, will function perfectly on anything other than the original Intel Mac Mini.
Hey, guess which generation of Mac Mini I bought when it first came out? 🙄
Heh but no in all seriousness, the configuration you're describing will run both apps perfectly well, even (dare I say) at the same time*
*not in any way guaranteed by myself. This depends entirely on what other apps you are running at the time, how well charged your battery is, what power settings you use, what hardware you are using to shoot video and record sound, and other factors. Refer to operators manual for exact specifications and requirements.