hmmm....not sure, but I think you probably could manage a part time job during the flying stages, but whether you could get enough hours to make it worthwhile is a different kettle of fish (I'm just thinking in terms of if you could only manage one shift a week, earning (Say) £25, would that be enough to justify the extra working time, or would you be better off just using that time to revise [for interviews etc], prepare CVs, checklists etc.)
Probably can be done in flying phase, but play very much by ear and be careful!