If I have a mirrored RAID set up, do I even need to use Time Machine?
YES. As someone who used to use RAID, let me tell you RAID only protects you against a very small subset of possible data problems.
Drive gone bad? Check.
Accidentally deleted something you want to keep? Nope.
Overwritten an old file? Nope.
Slow progressive data corruption that you don't catch till it's too late? Nope.
Made a change to a document, photo or a video, saved, then thought 'oops?' Nope.
Mythical Mac virus actually arrives and deletes your files? Nope.
RAID won't help with these. Time Machine does.