It's absolutely a problem I've had. I drove on a flat for several miles one winter because I thought the sound was just snow packed into the wheel-well, and driving on snow masked the funny handling characteristics of a flat tire.

By the time I got where I was going, the sidewalls were wrecked. TPMS would've saved me a tire AND a bunch of hassle of getting it replaced; the puncture was small and would've been easy to plug if I'd only known to look for it.