When playing a recorded TV broadcast on my PC, I notice heavy disk reads,
judging by the light on my HDD.
If they're heavy, you might need to defrag the disk, get a
newer faster drive, or record at a lower bitrate. Depends
on specifics but generally if you notice no playback
stuttering it's probably fine.
Will this stress the disk,
Of course it'll stress the disk, everything that reads and
writes stresses it, compared to having your PC turned off.
That stress is going to wear it out over several years of
use... what a hard drive is meant for, writing and reading
files.
or lead to premature failure?
No premature failure, there's nothing premature about
wearing out a mechanical device by using it. Similarly,
driving your car around town is a lot more stressful to it
than leaving it off and parked in the driveway, but that's
the point of having a car.