But I'm not 1000% sure. I know that FCP7 with DV material (on a DV timeline - with no effects) would not recompress anything - it would be nearly the same file.
You could try dragging a clip and letting FCP conform the timeline to match the footage - warning - this will be a non-standard sequence. You may get RED/render audio - but as long as the video is gray (not green), FCP is handling it natively (which many people will advise against - h.264 isn't a stable codec for FCP7 to work in.)
Add your titles at the end as planned. (Punch the production company in the face for not giving you editable masters.) Export a QuickTime file - I think it'll have to be a QuickTime h.264 and not an MPEG4 file - but it MAY work.
Surprise, surprise- it actually worked perfectly. I just had to make sure all of the sequence settings matched the H.264 to a T. Makes sense that the timeline will only spit out what is there- if what is on the timeline matches the settings- then no re-compression. I also just threw in a bumper that was full res and it rendered to match the H.264 quickly. While this is merely simple text, it exported quite clean.
My client relies on me to negotiate with a lot of amateur directors- so no punch needed. But it wouldn't surprise how many 'sorry but you sent me a compressed video' emails I have had to send out over the last few years.