The underside of the GP typically droops at the sides, and the sensitivity and structure tends to change as well.
The coverage, as far as signal levels go, goes out to eight degrees azimuth to either side, but the GP will often not be pretty that far out, even if it is usable. This is highly site dependent.
Even though the GP should be checked to safeguard GP interception all the way out to the coverage limits, I'd make sure to follow the book and be on the LOC before descending below MSA on the glide.