Having done many practice approaches in the Denver area, including flying through the localizer while on a vectors toward the mountains, this is very close to exactly what I had in mind when I read the OP's question the first time.Agreed, while on a vector. After being cleared enroute (direct to FIX), it isn't the same thing anymore--you're on your own navigation to your clearance limit not ATC's.
Very good example you pose, which I'll answer by way of a recurrent training scenario at Flight Safety International once upon a time in one of my previous lives:
After departing Stapleton westbound on a SID the CFI began a non-stop dialog with phantom aircraft for 10 minutes, preventing us from calling on frequency. Quite an impressive performance. At 10 minutes I climbed to the published lost comm altitude, whereupon he broke out in accolades for a job well done. Shucks, it was nothin'. I wasn't going to try to move the Rocky Mountains even in a sim.
dtuuri
So much of the answer to what to do is based on having situational awareness.