The only problem I see is if (after a serious incident) the logbooks are looked at
Are they? My experience (only a one off though) is that pilot logbooks are not looked at, other than to determine necessary extra ratings (like the FAA high-perf signoff). And anyway in this case the loss adjuster would look only at the club member's logbook (he has no idea that somebody else was looking at logging the time instead) and hopefully there won't be an entry there at all; the member will just say he forgot to log it.
However, there is a practical problem with all this, and that is if somebody gets injured. People then change, and if somebody can drop you in the s*** and get a better insurance payout, they generally will. But this thread was about legality.
I was always given the example of the Graham Hill crash where the insurers failed to pay out.
I have tried but never found out why they didn't pay out. It was said his CofA was invalid but why? GH was not short of money and being an "engineer type" was not unattentive to detail. I wonder if somehow the plane was not U.S. citizen owned? There isn't much that can invalidate a U.S. CofA because it runs indefinitely. The aircraft needs a release to service (Annual) but that's pretty obvious.