In a general sense, it is absolutely possible to play as a solo Cleric. While being able to solo things like the level dungeons and Challenge Mode up to stage 5 does take some decent equipment investment, it’s not at all out of reach.
Personally, I haven’t played as a fresh new Cleric in recent years. I’ve always had the same one Cleric ever since the Founder’s Server, so I’ve been slowly gearing it up into a fairly decent character over the years. However, I do believe that there’s a decent variety of Cleric builds that can solo most of the game’s PvE content all the way to the level cap. It just requires more investment to solo said content instead of completing it in a group.
At any rate, not being able to solo the level dungeons isn’t the end of the world. At some point, they don’t even give any exp or silver worth mentioning, and eventually they don’t give either at all. As for Challenge Mode, the gear requirement to solo it is a bit higher, but if all you’re looking for is exp, then I’m sure you wouldn’t mind losing a cut of some of the silver and items you get from it by completing it with a group.
I guess it’s also worth noting that the game just gives you some decent lvl 380 gear after completing a certain quest.