That's quite a jump from two flights a week at the moment up to two flights a day! From what I can see, the easyJet loads aren't bad but they're not exactly beating passengers away with a sharp stick - I'd say running at about 60-65% load factor on average on both routes. The other thing to consider is that fares aren't really increasing much towards the day of departure so average yields won't be great. It's not a disaster zone but I can't see that it's really as marvellous as some are making out.
LM were nightstopping a 145 in Southampton over the summer for an early morning northbound to Edinburgh so I guess there's no reason they couldn't do the same but fly to Manchester in the morning instead - if they chose to. The real question is, will they? To be remotely competitive with the train service, the route needs a decent frequency of service. There are some very busy days in the Port of Southampton - predominantly Saturdays and Sundays - but also some very dead days. Take Wednesdays next year. Two Fred Olsen cruise ships in on Wednesday 17 April but nothing on any other Wednesday in April. How do you plan an airline schedule to service that? [Hint: you don't. You fly frequently and then coincide with any sailings no matter what length.]