Leaning basic theory will always help a player regardless of instrument because there are general patterns in music that are prevalent including scales, chords, and progressions. The ability to recognize these common patters this will allow you to group songs that utilize these patterns to aid in memorizing songs because instead of remembering a group of notes or chords in a progression you can recognize this song has a common pattern and just remember the pattern instead of the individual notes.
Most musicians that go out and within a month play 100+ songs for events have a binder full of Lead Sheets which have the bare bones of the song including key, chords, and lyrics. These are not meant to notate the whole song, but instead used to serve as a road map of the song. Typically if a musician has Lead Sheets and can hear the song in their head they can play the song without any problems.
Solos are a different story, but most of the time especially in Rock and Pop the solo can be improvised. It is very rare that preforming musicians will play every solo exactly like the original recordings.