Denti:
That depends on type. Some do.
Speaking of only U.S. TERPS, the lateral limits of all LNAV or LNAV/VNAV IAPs do reduce in width from the FAF to the runway, but not anywhere near the lateral reduction of ILS or LPV/LP. I am referring to protected airspace.
Now, if you are speaking of avionics performance, some WAAS avionics increase the lateral sensitivity to ILS-like widths at the runway, but the integrity and alerting remain at LNAV specs: +/- 0.3 n.m. ILS and LPV/LP are far narrower than that at the runway.