Scouts will be at the college world series regionals and supers. Scouts will be at college conference playoffs. They will be at regular and non-conference games. They will scout right up to the when the draft boards are set. (well, maybe the day before).
I haven't heard of a pre-draft showcase for college players, unless you are talking about an invite workout by a MLB team. Every game a player plays is a "showcase" in college.
There is still a lot of baseball to be played before June. The scouts will figure out the pitching rotation.
Or, the scouts could ask him to throw a bull-pen before a game if he isn't pitching that day.
FWIW - Son got invited to a workout for XXX MLB team. His agent "highly suggested" he not go.....that it would show "favoritism" to that team since he didn't go to the other MLB workouts that he had been invited to due to his college playoffs. The XXX scout was everywhere and had already seen him play dozens of times.
In the end, it didn't matter. Got drafted by YYY team.