I guess you'd probably need to install a Mac OS driver from here -
so you can select an input in Logic, other than that setup doesn't differ much from using a MDI keyboard. I don't know how well MIDI guitar controllers work these days - thay used to produce a lot of spurious notes, which had to be filtered out below a certain velocity or deleted after recording, but my one time experience was quite some time ago; you may get some more experienced user advice with a bit of luck, though the forum seems to be a bit sparse these days. A post on LogicProHelp might yield results also, if you need any more help.
And you'll need to record a MIDI track first, which can then be bounced, if you want an audio file.
Your advice was insightful. The key was to go online, download and install the GR-55 Driver for OS X Lion. After that, I was instantly up and running. The connection runs quite seemlessly and the hardware/software are talking to each other like old friends. The USB connectivity sends and receives both audio and midi signals. This opens a whole new chapter in composing for me.