Yes, they can.
Remember, a paladin doesn't have to be a member of a church to get their abilities, though many are. As long as the paladin maintains his own lawful good and honorable standing, then he can attend whatever services he so desires. Of course, that being said not all gods or faiths would really uh.. fit.. for a paladin. St Cuthbert, Wee Jas? No problems there. Obad-Hai? Bit wonky but doable. Nerull, Hextor... uh... no.
Though thru proper background anything's possible I suppose. To use the FR setting as an example, it could be doable in theory to have a paladin that was born and raised in Zhentil Keep, as a Banite, and has since moved on to nicer, more socially acceptable things. But he still knows his way around the Banite faith like it's the back of his hand, and he could still claim to be a Bane worshipper... just non-practicing. More of an Ex-Banite, getting his paladin stuff from another source.