to be honest the only song i managed to learn completley with all the solos and everything was "you shook me all night long" by ac/dc. that doesnt mean i cant play other things, but i always prefer to learn only the small riffs or licks that i'll be able to use later.
it all depends on the style of a player you want to be, i think its very important to learn theory in the begining, but it wont do any bad if you'll learn few songs here and there, because learning just the theory is like learning how to drive, but without even sitting in the car.
of course if you want to impress the people around you should realy learn few songs, but i dont think it matters that much. the ammount of songs you know wont make you better, the whole point of learning songs is to learn how to write your own stuff while using things you learned from others