Hell vs. Baator

In large part, the nature of "faithless" depends on the pantheon rather than the laws of the Planes. In Toril, the Faithless go to the Gray Waste (assuming one still attaches the Planescape cosmology to Toril), where I believe they were used as bricks for the wall surrounding the City of the Dead under Myrkul's and Cyric's reigns. I am not certain what the ultimate fate for the faithless is under Kelemvor, but I believe it is not the wall anymore.

For Earth, and three of its most prominent religions, Baator is the most likely place "faithless" go. Baator is a rather unabashed clone of Dante's Inferno in many respects (and Celestia his Paradiso -- neither of these are exact copies but there's a clear parallel), so it serves to stand that nonbelievers would go to Baator in death. It's a little more difficult to qualify on Earth than Toril, however. On Toril, at least, everyone's deities do exist and everyone knows it, and when you die, you go to your god's realm, regardless of alignment, as long as you do not blaspheme your god. On Earth, there is no such universally accepted truth, so the above is based on an assumption that Judeo-Christian mythology is correct. If Hindu mythology or Hellenistic mythology or any number of other beliefs is the correct one, then that mythology would dictate what happens to faithless souls.

Simply put, it is very possible for a god to capture faithless souls and torment them in the afterlife. However, I do not believe that the gods can simply take any petitioner souls they wish. I would say it is largely dependent on the individual mortal's beliefs and the beliefs of those around him. An experienced planar need not worship or even believe in a deity to go to Elysium when he passes on. He only needs to be a good person. The worship is irrelevant. On the other hand, a prime from Toril that dies without faith would have ended up in Myrkul's or Cyric's wall. So, Phlotus could indeed claim souls for his own, but only if they were on the relevant Prime or involved with his pantheon somehow.

One way in which a god might be able to collect souls opposed to his alignment is if those souls in life defined themselves not by attachment to another alignment or religion, but by opposition to that god's views in particular. If one doesn't care about "doing evil" in general, but has a personal hate-on for a particular god's believers and clergy and philosophy, a pantheon might collectively agree that that soul could be taken and punished by a particular good god, perhaps with the possibility of ultimately cleansing him or releasing him to an afterlife more suited to his alignment after a prescribed length of time.

(Which leads to the interesting scenario that someone who wasn't motivated so much by doing good in general, as by destroying and negating the works of some particular evil deity, might have the pantheon require that deity to host that soul in a state of paradise within his evil domain! From such a vantage, the soul might be able to continue his holy war, protected from retaliation, in the afterlife, until he seeks rest or becomes corrupted by his environment.)