Off-pitch sounds incredibly sour together with any other music - nails on chalkboard level for some people. If it's only you, you do whatever you want. Still can't hurt to be conscientious, though: it's only a few strings, it's not like you're tuning a harp or piano or something. You will also be practicing both your tuning skills and, as indigo points out, probably also listening skills/pitch sensitivity.

Also, strings are likely much stronger than you give them credit for - tuning up a fresh string can stress it depending on material, but once it's "broken in", don't worry about it.