
Yes, if your healer is low on mana, play it. SMN and BLM generally don't need it whatsoever, especially BLM. TP songs can be handy when you don't have invigorate, and need a few ticks of TP. It's still better to do SOME damage then none due to having no TP. Also if your tank died, it may help to give them TP song, seeming they will be trying to get the boss/mobs back asap, and need TP for that. As well, you can always boost your MP/TP song once every 5 mins till the healers/melee/tanks are back onto their feet, so you don't have to sing that long. You just have to keep an eye out onto your party really. (Really, if you didn't get invigorate from Lancer yet, get it. It is GODLIKE for any melee class)
In fact, you'd be a terrible part if you didn't do the supporting of your class
Generally at the start of a fight, you pop your Foes Requiem (you can boost it as well if you dare to, but if you don't want to and save it in case you wanna boost MP song, that's fine as well), so by the time your healer possibly need mana, you got plenty again to restore his in return
In truth, in most dungeons you don't need to MP/TP songs, its more needed for raids. Foes is always a plus to use on boss fights, and even between packs if you have a magic users like a BLM/SMN with you, but you kinda need to learn the dungeon, and the class, if you wanna juggle your mana properly.
I'd play it safe and just Foes at the start of boss fights only, until you kinda get used to your MP management yourself ^^
In fact, you'd be a terrible part if you didn't do the supporting of your class

Generally at the start of a fight, you pop your Foes Requiem (you can boost it as well if you dare to, but if you don't want to and save it in case you wanna boost MP song, that's fine as well), so by the time your healer possibly need mana, you got plenty again to restore his in return

I'd play it safe and just Foes at the start of boss fights only, until you kinda get used to your MP management yourself ^^