How important it is to memorize a song all depends on your goal with the guitar, if you plan to go play in a band at some point or going to join jamming sessions then you need to memorize a lot of songs, it just doesn't look good on a gig if somebody in the band has to look at the tabs all the time.

I knew people that played perfectly with the tabs in front of them but from the moment you took the tabs a way they stopped playing simply because they didn't really know the song.

If you know the song out of your head then that is where the freedom of improvisation can start, not if you are to occupied looking at a paper sheet.

Herman