I think there is 9V on that line that feeds the regulator in the head unit. AFAIK nothing uses 9V but there is a linear regulator to supply the 5V, which if it's a typical 78L05 sorta thing it will remain in spec down to about 7V supply before the regulated side dips. Things might even run significantly below 5V, too.
If you're talking regular Cat-5 cable you're looking at probably 26AWG with a load of maybe a few watts, say 1A for nice numbers. You're looking at maybe 40 milliohms per foot, so 100' is 4 ohms, which is 4V at 1A, which puts the 9V at 5V, which means the linear will probably be well below 5V. I think that load is probably an over estimate, although with the backlight and everything, I dunno.
Signaling-wise, I think it's just a twisted pair serial protocol, so 100' might be OK depending on drive strength. You'd have to look at the schematic to tell what driver they are using. I'd bet it would work alright, but 100' is pretty long.
I can tell you this, the control cable for the FC-40 works fine at 50'. It's got 13.8V on it, not 9V, though. I'd suspect that the FC-40 is designed to operate at a wider swing since it's assumed that your radio would be operating probably at 12.2V minimum, 13.8V nominal. So it can deal with probably a cable drop on the order of 5V.
BTW, you don't need to do the wide copper strips for VHF FM, though it can't hurt. Grounding is about references and as long as everything is referenced to the same ground then you won't create a loop. The problem would be more difficult with an earth referenced antenna, which most likely (just guessing) your VHF is not. It's probably got it's own radials (particularly since it's mounted high, there is not much chance of it coupling to earth). Point is a 100 foot long ground conductor is fine as long as your radio, power supply and antenna grounds all connect together at the same spot only and then there's only one path back to earth.
Now the idea of a shorter coax is very valid. Interesting. This is probably the best reasoning for doing this, or at least some combination that does work, like 50' of control cable allowing a 50' reduction in coax. BTW, you ARE using RG-8 for this, right? RG-8X and RG-58 have ridiculous losses at >50MHz. :-)
"Stand your ground. Don't fire unless fired upon, but if they mean to have a war, let it begin here." -- Capt. John Parker