Good Boy Skip

It is possible to skip the first phase of the Wily fight through Rush Search breaking you out of the cutscene.

To break out the cutscene you need to get a drop that fills one of Mega Man's energy meters. Rush Search itself will get you missing weapon energy, but your odds of breaking out go up if you do not have full HP. Even 1 missing HP is enough.

According to PJ, there are three columns of "dark purple" like the one above Mega Man in the image above. The third one is when you want to summon Rush Search to make Rush actually spawn.

If you get a life or ammo drop, You will regain control of Mega Man. Much like the Turbo Man quick kill, you can damage the boss the moment it has 1 HP. This can be any weapon that does enough damage to reduce the machine to 0 HP, though timing can be tight.