Yes, you will, otherwise the texture will be 'depressed' where there are, well ..., depressions/tears in the wall. IF you texture, you can certainly 'cut corners' and not have to do as nice a job but most likely, YOU will notice any slight imperfection.
I understand your situation and empathize. However, a job that's half-prepared will look half-finished when it's 'done'. For me, the decision is easy. Just understand that you have to 'live' with whatever you end up doing. And if that's all that matters, you're certainly in a position to do what you want to do. I do wish you well.
My best to ya and hope this helps.
Jay J -Moderator
PS: Do you know anyone in the Trades? Of do you know any family or friends who may know someone in the Trades? Your type of 'job' is really an easy side-job and not that expensive. When you find someone, ask them what YOU can do to cut the cost down. And lastly, BEFORE you put any paint on the wall(s), be sure to PRIME/SEAL the entire wall with a relatively heavy coat of PRIMER/SEALER.