You absolutely can. The biggest difference is that you’re going to lack the mana sustainability of someone that’s heal spec’d.
You’re likely going to need to drink a lot - and you might need to ask your group to use CC or do slightly smaller pulls, depending on how well geared you all are. Especially in the higher level dungeons.
I’ve never done solo-questing as Resto in TBC, but from what I’ve heard it’s pretty dire. You can definitely do it but you’re going to have a very slow kill speed alongside mana issues. I think you’d probably be best going Elemental (even for healing) until maybe at least the mid 60’s, then switching to Resto once healing starts getting too difficult for Elemental to cover.
Had multiple healers off spec healing me (feral druid) during leveling and barely any issues. Only clutch moment I can recall was doing Shadow labs @ level 68 and only issue was the first boss.
That being said I would only consider leveling in healing spec when doing 5 man premade dungeon leveling.
I level as shadow priest and heal dungeons, it gets more difficult the higher level you get.
You will need to drink a lot more often, and probably use mana potions on bosses. What made vanilla easy was that you could downrank and play more effectively than intended. In TBC this is no longer possible. And healer output is pretty much normalised.
I have GOOD healer gear (T2 and Naxx gear) yet if the party contains a badly geared tank and crappy DPS, making dmg intake higher and fights last longer, its gonna be a challenge.
Still it is doable. However if you’re gonna be enhancement and have almost no real healer gear, it will fail unless you get a really good group ofcourse.
If you wanna level a priest and occasionally heal dungeons, Id recommend trying 23/x/5. Down to improved divine spirit in disc, 5/5 spirit tap shadow, and rest in holy so you get spiritual guidance and surge of light. It does close to shadows dmg, and you barely ever have to drink. If your gear is stacked with spirit and crit you might even do higher dmg than shadow on short 1 by 1 mob fights.