Do you HAVE to? No. Would it be helpful? Definitely.

I used to feel the same way as the OP, not really interested in DPSing (afterall, I became a healer to HEAL, right?), but one day I was a bit bored in low level roulette so I decided the throw out some DPS and I found that it added a whole new dynamic to my class that I had completely ignored up until that point.

Now I will always try to throw out some DoTs/Damage whenever I have some spare GCDs, cos it makes the the game more engaging.

TL;DR - Give it a try, you may just enjoy it.