Possibly, I just sent my Edge 500 to them for repair, 2 years out of warranty, the guy on the phone said they would cover the breakage as an act of good will unless they have good reason to believe the damage is crash damage.
Which Garmin strap is it? There are more than 1 type.
It's not the premium but the one with a hard centre and two plastic sensors either side.
Yeah they should do, i had one replaced about a month ago and it was the replacement for the replacement so at least a couple of years old.
I'll give them a ring and see what they say.