Given the existence of hit dice? Yes. And given I've been playing for about 18 months now, I feel pretty confident saying any flavor of Cleric will do just fine n 5e. In fact one complaint about the game by some is it has too much healing, which resulted in options in the DMG to reduce healing. I've yet to hear anyone complain there is not enough healing in the game.
Just covering another aspect linked to the theme of "do I have enough spells outside healing as a non-life cleric":
Again, from someone only just starting with 5E, and coming from PF, the number of spells available per long rest seems to be quite a bit smaller, considering that in PF/3.5 you also have bonus spells due to domain and primary casting stat.
We regularly go through 3-4 major fights before resting or retreating in PF. Typically, in the last 1-2 fights the magic casters are quite powered out. The fighters are usually OK due to CLW wand heal spamming.
In 5E, at mid levels (7+), features such as second wind or healing do no seem to give back enough HP between fights to enable a tank for recover to (almost) full HP between difficult battles. In which case he will need assistance form the healer in form of spells - not speaking about slots used up alread in-combat healing...
Just trying to get a better sense of how this works in practice in 5E... i.e. suppose there are 3-4 or more major fights in a "workday" with perhaps 1-2 short rests. The amount of healing or magic power (and HP for fighters) recovered during short rest seems to be not very much if the party is down to the last HPs after each fight...
Seems to me that in the 3rd or 4th fight, the cleric may well be swinging his weapon and not doing very much else (any cleric for that matter...)?