Regeneration is lofty, although I think you're being semantic - a 'boost' might be fairer as Northampton does have pretty bad rail service.
A train to Oxford won't transform the city in isolation, but it will definitely give it better connections for various things. Shopping at Bicester and many jobs in and around Oxford, as well as education, culture, leisure and onward connections to the West of England.
One might not commute that daily (who is doing that anyway) - but for meetings, or more occasional business travel, it could be useful. Oxford has one of the healthiest economies, especially for the smaller cities.
Similarly as to why I mentioned Corby, Kettering and Wellingborough... Northampton only really has radial links out of London. Mixing that up is only a benefit to people across the South Midlands - which is a high growth area - and the many things they might do, and travel for. And drive to otherwise.