In savage raids yes healers should be contributing to the dps as much as they can without compromising the primary role.

In expert/dungeons/trails and such. Not so much.

The key thing in mind is you should always be casting. Be it healing up the tank, apply regen to the party, shielding up for damage or throwing out dots and your basic dps move if party health allows it. You should never just be standing there waiting to heal.

A it a sign of a bad healer/lazy player and b its just bad manners to the party.

If your new to content your other healer may be willing to shoulder most of the role so you can learn the fight but you should do the minimal you can to help. Be it keeping up party regen/shields and applying dots. Once you know the fight try weaving in some dps between the difficult mechanics and your normal role requirements until your more confident. Best thing you can do is communicate with your other healer and tank to gauge there abilities.

Im quite lucky I run most content with my co healer...this tend to turn into 'you do all the healing ~I'm dpsing lol.'