Afraid not. May not be any faster than in the days of CIGs/REPs or even CORs but a quick comparison with 1970-ish shows:
Portsmouth same with 1-2 extra stops, Weymouth same, Exeter same as Warship timings but extra stops , Bournemouth 5 mins slower with 3-4 extra stops.
Best steam timing was 2hr Bournemouth and 3hr Weymouth - only Exeter was faster (by the ACE).
Still, I agree the Southern isn't known for high speed....
Portsmouth used to be 1h 25 - 1h 29 (fast) and they used to be:
Woking - Guildford - Haslemere - Havant - Portsmouth S/Sea, some stopped at Petersfield.
They most certainly didn't follow the stopper, like they do now or sit on Havant Jn for 4 or 5 mins on a regular basis like they do now.
The SW Portsmouth line timetable needs a radical overhaul because you can do many journeys quicker and more easily by road. I can do where I live to Southampton quicker than not by road than by train, A3, M27.
That's because the train often sits on Woking Jn for something to cross and so misses the connection there.
I have a TOC card, I never use it because its so slow & the network is so poor that I prefer to drive.