What if a pilonidal cyst pops on it own?

That would be a : Fairly normal course of events for it to relieve the buildup of pressure from the infected material creating an exit pathway or sinus. Without treatment this scenario may often recur.

Temporary relief : If it pops and drains you may feel better within a few days. This takes the pressure of and may help the Acute infection. If you're lucky it won't flare up again for a few years. However, if you don't have the cyst excised it can recur over and over again.