I've had this. It didn't work in so far as I went on to need ivf, but glad I had it anyway. My consultant found I had a blocked tube and widespread endometriosis which he sapped away whilst in there, so who know whether clearing all of that up helped with successful FET (had a freeze all IVF cycle due to OHSS - oh PCOS, the syndrome that keeps on giving!)
In terms of recovery, I had the lap on the Friday, and was back at work on Monday. To be honest I was only pain free by the weds, but I was 2 weeks into a new job so just sucked it up. Codeine and walk very slowly. Was very swollen afterwards, but that was due to the extent of bruising caused by endo removal.
The drilling should take about 15 mins but I was down for 45 as he was doing the rest.
I would 100% have this operation in your shoes; it might mean you can avoid IVF, which would be obviously ideal. Professor Robert Winston recommends this for all PCOS women who are struggling as the procedure to do prior to going down the ivf route - most people don't get to try it, NHS pushes them straight to ivf.
Have you been prescribed metformin too? Ask your consultant about it, as t can be used off-label to promote fertility.
and good luck.