After getting out the scrub brush and removing a few posts...
This is in no way an "official" response. However, after doing some checking it seems that indeed, FoTs will do a relatively small amount of damage. "Relatively small" means "individually". This is a remainder from back before they were changed so that players could no longer be stun or flop-locked in place by a group of FoTs. I don't recall precisely when, but that change happened some time last year. Before, you could be locked in place by a group of strategically-placed FoTs and left to die, wait for rescue by a guildie, or be forced to leave Siege, if only temporarily. The FoTs would slowly damage a toon, and it seems that the more FoTs there were in the area of effect, the more damage you took.
These days, you could have 20 or so FoTs placed around you and you will flop for 10-15 seconds, then gain a 30-second immunity from them so you can get out of the area of effect. Unless you pay specific attention, you'll probably not notice having taken damage.
Others have stated that an FoT will eventually kill a floating balloon, which is quite true. So it would be reasonable to expect that 20 or 30 FoTs placed next to a gate or other castle building would eventually do enough damage to the structure to destroy it. And apparently, the damage effect is either additive or multiplicative, so the more FoTs there are doing damage to the structure, the faster the damage accrues.
Personally, and speaking solely as a player, I don't see this as being a huge issue. There are any number of ways to defend against and mitigate the tactic. That's all I have to say on the subject.
I will remind people that if you intend to discuss this further, please follow the forum rules. That includes discussing or describing recognized exploits, as well as staying on topic and treating others with respect--no personal attacks, flames, et cetera.