It might work, but it will have very limited directionality.
A big loop around that fence might actually work a LOT better: And it won't have moving parts to mess with. And will be cheaper. And less noticed. HOA Jackboots and Gladys Cravitz Busybody Types may be about. Certain HOA Goons are now using Selfie Sticks to infringe on homeowners privacy rights where they raise the selfie stick RIGHT OVER YOUR FENCE, I kid you not, you can find them (and a LOT of really pissed off homeowners) on youtube when it comes to HOAs, despite the few Disgusting HOA Apologist Lap Dog Types who lurk here on eham.net and talk crap. Don't be a Victim- Forewarned is Forearmed!
For a vertical, consider a small one... even a mobile, and put lots of radials under it. This is where YOU have a fantastic advantage! No one has ever fallen to their Death from radials being laid on the ground, either... Nor do they come down in bad weather. Though I've tripped over a few... ;-) The radials do NOT have to be in a fan arrangement directly under the driven element. On a corner, just lay them out, the more the merrier, but even ONE will work. (Which is how the "Paliepole" Vertical works...)
SURE more radials work better, and SURE they work best fanned out in a circle, and SURE your signal is going to somewhat be "bent" with corner radials. But they'll WORK. Better than you think!
If you have an "edge" on say the side of your house, run a vertical element up there. You can even bend the last part of it to up the side of the roof. Or "caulk one in" on a nonmetallic edge. Much like the radials, the vertical radiating element does NOT have to be perfectly straight!!!
But I'd try the loop first, if I was in your shoes. It may be electrically QUIETER than the vertical anyway. With a good s/n ratio, you can HEAR THEM better.
You might even put up BOTH types of antennas and have fun with an "AB" comparison!
I wouldn't worry about the measurement of the loop, either. Just a big loop around the whole fence, feedline (not coax if you can, or just a short one if you must) feed it at the corner with an autotuner (preferably weatherproof grade and stick it in a box/shed or hey you could even bury it (again!) if you are dealing with SS Grade HOA Antenna Nazis, even one of those fake plastic rocks (in the city you can hide one in a Telco box... they're easy to obtain or just take a plastic grey box and put a logo on it or something.)
An autotuner can also go into a plastic trash barrel and the feedline can run into the dwelling through an already existing access. (They always drill them out too much so there's almost always space there and then there's also dryer ducts that aren't really dryer ducts... ;-))
If you go the vertical route: Don't attract a bunch of attention to yourself! And don't try to do this at night, because if you think that this is the best time to pull of an antenna installation, then you've watched too many Hogan's Heroes reruns. A couple of your buddies, a van, and a couple of hard hats can easily do this for you. THEY WON'T LOOK OUT OF PLACE PRECISELY BECAUSE THEY ARE UNFAMILIAR! They just show up, in daylight, best time is just after the HOA office has closed say on a Friday, or even on a lunch hour. Trust me on this, and read my other posts.
And you'll be in a position someday to be a "construction worker" at THEIR respective QTH's. No Ham tags, just get in and get out: You can gloat like 'mutas over beers later. And you will! If you thought Antenna Raising Parties were fun, well COVERT Antenna Raising Parties are a blast!
Look at my logbook. You can work everywhere QRP. Despite the sunspots. Despite the glossy ads for "Steped on an Infrared" and "Hi Flashover" Antennas , and Shooting Star Antennas, and The Hustle Antenna. (No doubt someday they will be monthly centerfolds... Have you laid eyes on the "Miss February" Antenna yet?) It's not a boast: EVERY QRP Op knows it and does it!
Good Luck and
73! Let us know how it worked! You can see my very modest vertical mobile on a tripod home setup by looking me up on QRZ.
OR let me know by direct email w8lv (at sign you know what to do)arrl dot goes here net.
Caveat Emptor. NoTrademark was infringed upon in the writing of this message.
DE W8LV BILL