I would just point out that virtually all mortgage lenders require that the borrower provide a "gift letter" if gifted funds are being used for a down payment.
Using gifted funds for a down payment can definitely have an effect on mortgage approval.
That is absolutely correct but is also absolutely irrelevant for the purposes of this discussion, which concerns the annual gift tax exclusion and the preparation and filing of gift tax returns.
As @jtax pointed out earlier, the gift is complete once the funds hit the donee's account. It would still be considered a completed gift even if the mortgage was not approved (absent an agreement to the contrary).