Whilst an engineering degree will not do you any harm, I don’t think that it will greatly enhance your prospects of landing a flying job.
You really do need to be aware of what you would be getting into, an engineering degree is incredibly challenging. When I was going through my BEng in the UK, the engineering degrees had the highest drop out rate of all academic courses.
Of course any academic qualification is of limited use if you do not have reasonable experience actually working in the subject area after finishing the degree. Your prospects of landing non flying employment as a back up plan while you’re looking for a flying job will be better with an engineering degree than a social sciences degree as the engineering degree lends itself to more careers than the social sciences degree. However when looking for non flying work keep any reference to a CPL off your CV as if a potential employer gets an idea that you are a qualified pilot ready to quit their company at the first sign of a flying job they won’t be interested in you.
Good luck with whatever you decide to do.