Can the person who built a payment run approve it?

Yes, unless your company switched on Someone else must approve a supplier payment run (off by default — warn, don't block). With it off, the builder may approve and the trail records it as self-approved. With it on, the builder, the person who sent it for approval and the person who last changed its bills may not approve or reject it — You built this run, so somebody else has to approve it — Owner included; and a run with no recorded builder cannot be approved. Set it on Settings → Payment approval.