git: can I checkout a hotfix branch in a dev environment(with an unmerged dev branch) or will that cross branches?

git: can I checkout a hotfix branch in a dev environment(with an unmerged
dev branch) or will that cross branches?

I'm new to having git set up for multiple users. I typically used it by
myself with only one branch. I have a questions that I couldn't find safe
answer to via Google:
If I'm currently pulling a feature development branch into my dev server
to test the feature and I suddenly discover the need for a hotfix can I
re-branch(checkout) the hotfix branch (part of master not dev), pull the
files in and start working on/testing a hotfix or will my next "git add ."
add the files from the feature branch(which are still on the server) to
the hotfix branch therefore mixing the two branches?