Even if the TG fare isn't supposed to earn status or accrual miles, you should still hand over your MP card at check-in. TG often makes mistakes and will credit you miles anyway.
My favorite story is flying BKK-HKT on an award ticket. I intentionally scheduled an early Sunday return flight that I knew I was going to miss, only because all the awards seats were filled on the later flights. I figured I would just try to go standby on the later ones, even though award travel prohibits that. As it turns out, all the later flight were sold out. While a group of 20 people were waiting for standby tickets, only two seats in business opened up. Due to my 1K status, I lucked out and for $20 got one of the biz seats. When I checked my account a few days later, TG had actually given me the flight miles plus 25% biz bonus for the return leg of that award trip. ^