Hi,
Having entered Southampton to Salisbury Station into Google Maps departing now, it shows driving routes from 53 minutes to 1 hour 2 minutes (24.3 miles to 27.2 miles).
Obviously, it depends on where in Southampton you live, but you do seem to be on the cusp.
Furthermore, I find Google Maps to be a little optimistic if anything. If you can do it quicker because you exceed speed limits or "just catch" traffic lights before turning red, this would be a concern to railway recruitment teams.
You say that Salisbury is the nearest SWR depot to where you live:
SWR have a depot at Northam (Southampton) (
https://maps.app.goo.gl/s3c69qZrUXhGmfg67) (albeit, it's one of the smaller driver depots) (7-8 minutes or 1.1-1.6 miles)
Fratton depot (Portsmouth) is 45-48 mins (20.8-23.5 miles) from Southampton (obviously depends where in Southampton you live)
Hope this is helpful.