In nuclear reactions are all the species involved, naked nuclei that is, are they all atoms that have been completely stripped of their electrons? If not, then shouldn't an alpha decay result in the formation of an anion and shouldn't a beta decay result in a cation?
Nuclear reactions involve energies far greater than anything in chemistry. Whether or not the nuclei are stripped of their electrons, does not matter at all (except for electron capture, of course; to capture an electron, you must have one around in the first place).
So yes, a beta decay of a neutral atom does indeed result in a cation. As for alpha decay, here we have a massive particle leaving, so the remaining nucleus would be shoved in the opposite direction with considerable force, no doubt enough to break it free of any chemical bonds and strip it of quite a few outer electrons. If not for this factor, the process would leave behind an anion.