Does inserting part of the sock and then taking it out before completing wearing it count as having worn it while not in a state of ritual purity, thereby necessitating re-ablution to wipe over it?

The condition for wiping over socks is to put them on after completing ablution and washing the feet. If you insert part of your foot, then take it out, dry it, and reinsert it into the sock, this is considered putting them on after a complete ablution, and you are permitted to wipe over these socks.