Timing on an ILS
I was taught and trained my students to time on an ILS, as a backup for determining the MAP and to fly it as a LOC approach in case the GS goes out.
Illini and Batman raise interesting points, though, about whether you should complete the approach if you should lose the glideslope. I hadn't really thought about it before, but, I think, they're right. I'd take a miss and get a new approach clearance. I'd also report the GS outage to ATC. As George points out, correctly, you can be cleared for a LOC approach with the GS out of service.
Now, if you have an ILS/DME approach, you can time if you want, but you would determine the MAP with the DME. If you lose the DME during the approach, you have to take a miss and get a new approach clearance. The DME is a required component of the procedure.
Probably Dep676's friend busted not because he started the timer but because he went full deflection on the localizer. Assuming no other information, that sounds like a legitimate bust to me.