Sarah - such applications are not automatic so the entry will remain on the register until the form HR4 is processed.
The buyer may be willing, as you state, to still complete provided they have the decree absolute to confirm divorce and they do the normal checks to confirm your HR4 is in play
However if they won't then you/your ex/the conveyancer can
request that it is expedited to shorten the wait time to generally 2 weeks or less (usually much less)
If you have submitted a copy of the decree then the processing can be quick. If you've submitted a signed release for example then it will take longer as we will need to do wider checks to confirm ok to remove the entry.