I would say unlikely. I left the region 1st June this year and in late may we were having sunny morning but generally clouded over by midday. This was before the monsoon started. If you were going to try in June, I would propose very early June and summiting on sunrise.
Fall is better for peak bagging... Went to climb Ama Dablam last May (late May)... and as Radson said, the weather was pretty bad most actually all days. Some days it was already clouding up before 10:00am.