Yes - this works.
I had to do the same thing last year with an entire tape (a continuous seminar recording). The tape would only play back without dropouts using the camera's (XLH1) slow motion mode.
I set FCP to non-controllable device and hit capture now, then I played back the tape in slo-mo. I seem to remember I had to keep hitting the play button on the camera to keep it playing - maybe that depends how bad the issue is.
Only drawback - you don't get audio using this method. Luckily I had a 2nd angle that had an on-camera mike so I got away with it.
I found the sped-up clip very processor-intensive to work with so once I'd got the speed right I exported a Prores version.
Hope this helps!