The connection from Fareham (etc.) onto services via Gatwick Airport isn't ideal at 17 minutes. Typical journey times are around 30 minutes longer than today and applies in both directions.
Eastbound there's a connection at Hilsea which shaves off around 10 minutes. Westbound, it appears this connection, or one at Fratton, is not available. I don't think I'd really recommend changing at Hilsea though, apart from the down-at-heel nature of the local area and poor facilities, I don't think it's possible to get between the two platforms without using the stairs or undertaking an incredibly long walk via the main road?