Yes, you can be a pitcher and position player at the tryout and make the team.
My son had previously been LHP/RF/1st. He tried out for P/OF the first year and only P the second. It was a personal decision to focus on his best skill, which we felt was his future in baseball. He still does it all in HS, but no way he'd ever see the OF or 1st in college.
In looking back at the nine players from Tulsa who made the team, here's the breakdown:
Pitcher only - 2 (both LHP)
Catcher only - 1
P/IF - 1
P/C - 1
P/OF - 1
OF - 3
My numbers may not be exactly right. I'm going off my notes from almost a year ago, and they may not have been perfect even when they were fresh in my aging brain.