Can an ant etch a hole in a tent with formic acid?
I would be VERY surprised if it did. The answer depends on what material the tent is made of. Most tents now days are made of polyester and according to the table below (taken from: http://rfelektronik.se/manuals/Datasheets/solventguide.pdf) polyester has good resistance in formic acid (Note, S stands for satisfactory in table). 

However, even if it was nylon, unsatisfactory resistance means that the material will deteriorate in hours to weeks when used with the chemical. I dont think an ant or some ants would be able to produce enough acid to seriously damage the thick fibers of the tent. Maybe if a lot of ants were attacking the same spot one after the other you would eventually dissolve some of the nylon to make a small hole, you never know.

Also, an ant attacking a tent is a very unlikely scenario (ants use formic acid to defend themselves).