Yes, you can batch export from the browser without going to a project. Try it and see off there’s an acceptable format for you. I think you can only go to QuickTime using master file export and that doesn’t let you change the resolution.
Handbrake batch converts but unless you don't mind having video pulled from the bottom of the quality barrel I'd avoid using it. FCPX exports h264 files at around 10,000 mbps. I set Compressor to its max 19,453 on h264 files. Handbrake give you 6800 kbps (KILOBITS!)
There's a batch export out of either the browser or timeline in FCPX using COMMAND POST. (CP gets to a lot of hidden / unused parts of FC.) Scrolling timeline, pasteboard history, movable markers, and all other useful gems.
I batch convert Tricaster clips to H.264 for editing in FCPX with HandBreak a couple of times a week. I get great quality, faster than Compressor, love it. Personally, for this sort of thing, I'd recommend it over Compressor.