If easyJet expand their offering from SOU (and let's not get ahead of ourselves, I'd imagine they'll want to see GVA work first), then I think what they're most likely to do initially is drop flights in from existing bases or operate W-patterns rather than base aircraft at Southampton.
I think this for two reasons, one is the cost and hassle of setting up and maintaining a base, and SOU could only ever be a small one given the constraints on how many aircraft they could nightstop there, therefore it would lack the economies of scale available elsewhere.
The other is productivity. Given that Southampton closes overnight, in the event of delays to the schedule they would run the risk of not getting their based aircraft home at the end of the day and ending up either in BOH, LGW or BRS, and then having to position back the next morning. Added to that, the limited opening hours at SOU may mean that aircraft based there operate less sectors and are tucked up in bed earlier than their counterparts elsewhere, immediately rendering them less profitable.
What I think would work quite well would be a small number of core domestic routes (e.g. EDI, GLA, MAN, NCL, BFS) operating twice daily at breakfast and teatime, with international flights from European bases arriving during the day, say at a frequency of 3-5 per week per base, and then some additional sun flights to the Med arriving and departing in the evening.
Of course this could all be pie in the sky! No matter what happens I agree with everyone who says it's now time for SOU to invest airside and grasp the opportunities that are waiting.