Just because they issue the fine, don't mean they will be able to collect on it.
Sure they can. The government can make your existence totally and absolutely miserable if they want to. Especially if they want to make an example out of you (like they are planning to do to most of these folks).
Firstly, you already can't count on being able to fly again for a long time (if ever) as interfering with or assaulting a member of a flight crew gets you placed on a no-fly list along with the other terrorists. Failure to pay assessed fines will almost certainly keep you on the no-fly list indefinitely.
Then, when you give them the middle finger and don't pay, those fines were issued as a part of a legal process so you can be jailed for contempt and held as long as that judge wants to keep you there, no limits. I don't know for sure, but I suspect interest will accrue on past due unpaid fines so you'll eventually end up paying a lot more down the road. There is also the possibility that the FAA can issue additional financial penalties if you fail to pay. And, bankruptcy won't help, as those types of fines aren't ever subject to discharge in a bankruptcy proceeding.
They can also garnish your tax returns, and garnish your wages or any government payments you receive. Any garnishment orders your employer receives will include a copy of the original court order, so your employer will know exactly what you did and just may decide you are an employment risk and terminate your employment (this is far more likely if you happen to live in one of the at-will employment states). They can also put liens on your bank accounts, real estate, cars, and personal property (all of which will contribute to ruining your credit).
Since these types of fines also always accompany criminal penalties, failure to pay can get you thrown in jail instead of staying free on probation.
Plus, don't forget the airlines. Anytime they divert a flight to eject an idiot, it costs them tens of thousands of dollars. You can be sure you absolutely will be hearing from their lawyers on the subject. This is in addition to whatever the FAA does to you, and the airlines will hire whomever they need to in order to get their money.
So, what it all boils down to is, if you don't want to wear the mask, just drive there.