This seems to technically work but has a very limited benefit
Notably, for this to work at all you would have to reduce the Defender's bonus to zero, otherwise it would still have a bonus to its attack and damage rolls.
After this, you would be holding a Defender with no bonus to its attack and damage rolls; thus it seems that it would benefit from the Sharpen the Blade feature. This would grant the sword a +1, +2, or +3 bonus to its attack and damage rolls for 1 minute. Then, for the remainder of that turn, the Defender would grant a +3 to your AC. Then your next turn comes around and the Defender would gain its +3 bonus back which would stop Sharpen the Blade from doing anything as it would then be a weapon that already has a bonus to its attack and damage rolls.
Thus the only benefit this has is on attacks made on your turn using the Defender after the first attack. This is a rather small benefit, all things considered.
Sharpen the Blade might continue into future rounds, making the benefit greater
It's unclear to me, but it is possible that the Defender getting its +3 bonus back does not actually end Sharpen the Blade but instead halts its effects momentarily; meaning the Monk could repeatedly choose to have the weapon lose its +3 bonus and effectively give themself +1/+2/+3 to attack and damage rolls and +3 to AC for the cost of 3 ki points and a single bonus action. Does Sharpen the Blade having no effect mean it ends, or sits there dormant, and reactivates when the bonus is removed again? How this actually works, as with many other things, is going to be left to the GM.
I probably wouldn't allow this at my own tables
This enters that gimmicky level of play that I tend to avoid; where the small details of the wording of features that have nothing to do with each other is important. Combining them in this way goes against how I imagine the rules were intended to work. That said, I don't think allowing this would break the game either; it's merely moving around bonuses so that features actually do work together when they otherwise might not have. Perhaps I would try it out and see how it goes; after all the best way to learn the ramifications of a ruling is: Playtest! Playtest! Playtest!