If what you—as the DM—want is a ghost (Monster Manual 116–8) that possesses the feat Vow of Poverty (Book of Exalted Deeds 48) not to count its ghostly equipment against the vow's strictures, that's what should happen in your campaign. You know your campaign and your players better than outsiders.
Keep in mind, however, that the feat Vow of Poverty does say that the creature possessing the feat "may not use any magic item of any sort" (48 and emphasis mine), therefore the feat doesn't care if a magic item has or doesn't have a gp value (artifacts, for example, usually don't!) nor if a magic item is present on this plane or another nor even if a magic item is material or immaterial. Instead, the feat asks only Hey, is that a magic item you're using, dude-possessing-the-feat-Vow-of-Poverty? and if the answer is Yes then the vow is broken.
Thus, while the ghost that possesses the feat Vow of Poverty could—with the DM's approval (and there's a lot of that going on here, what with the creature being a ghost with the feat Vow of Poverty and all!)—carry around those "2d4 items that it particularly valued in life" (MM 118), if any of those valuables are magic items, the ghost can't actually use them without breaking its vow.
Note that this DM would be comfortable with the "swearing [of] a sacred vow… in the presence of a celestial being" (BE 39) allowing the ghost to abandon any ghostly equipment that violates its newly-gained Vow of Poverty feat. This DM might even be amenable to allowing the ghost to keep the some of the 2d4 immaterial and nonmagical items the ghost "valued in life" as a consequence of its immaterial nature. (Like maybe a freakin' holy symbol! I mean, c'mon!) However, I suspect the majority of DMs would equate owning an item (and the feat Vow of Poverty says that the vow-taker "must not own or use any material possessions," including not-really-material-possessions like grafts and contingent spells!) with retaining an item, ghostly equipment or not.