Would treating my tarp with permethrin help with mosquitos?

Permethrin doesn't really have a repellant effect unless insects touch it. They'll land on a treated surface and not really like the little dose of poison they're getting. Permethrin is most effective on clothing and *maybe* bug nets, but probably won't do much on a tarp.

Keeping the tarp low to the ground will do more than treating it, but I'd suggest treating your clothes and Meteor bivy, and actually using said bivy.

p-rin will eventually kill any mosquito that lands on the treated section of the tarp.
it will not repel them in any measurable way.
just exactly WHY, one is going into an an area rife with insects and living under a tarp in a bivy.. is another subject.

you can spray everything you want with p-rin, and it will reduce the number (but never to zero) of mosquitos.
p-rin may not help the coatings of your tarp. i think that it;s effect on silicone is null, but i suspect it to not help the polyurethanes very much. that is my unproven/undocumented op.
it's your gear. so, it's your risk.

me, i hose everything except the tent fly, and bugs are thusly greatly diminished.
p-rim will help, but not cure, the insect problem.

good luck !

peter v.