Generally speaking, especially with the 4e system, gods and divine characters have a seperation. The power comes from the gods/astral plane, but the gods don't really, for example, punish a paladin by taking away his powers. It's up to the various orders of faith to police themselves. So, at least as far as clerics and the like are, the gods mostly don't interfere in mortal matters, they basically let their churches decide who to induct into their order. Now, sending extraplanar creatures in, like angels, is a more direct intervention. And if you get to the point of epic tier adventures, you may actually have charcters getting caught up in the astral sea, and be involved in gods demons and devils vying for power, etc.
It's just as easy to refluff things like the Thor movie did ... the gods are extraplanar beings, in the same way that primordials are, and that fey creatures are, and that abberations are, etc. Basically, the astral plane is just another plane with powerful creatures there, and just like arcane power, or elemental power, or shadow power, or primal power... divine power is something that flows from that plane of exitence. The godhood is thus mostly the result of mythology. The first people to interact with beings from the astral sea were so awed by them, they worshiped them as gods.
It could be very easy to use the basic concepts and have gods that intervene, gods that don't intervene, or gods that don't exist as they are believed to (either there is nothing, it's just a power source tapped by the church who either don't know, or actively hide, that the gods are dead, absent or never existed ... or it could be that say ... demons, devils, primordials, creatures from the far realm, etc are pulling a scam, trading power for devotion). The church would likely present the same front regardless, but it would be easy to have a 'black box' approach to the divine power source (i.e. prayers go in, spell comes out, no one knows what happens in between). The epic tier adventures would be interesting, but then Dark Sun is able to handle Epic tier adventures without having to travel to the astral sea.