Small sample, but I looked up the ace pitchers on the final Top 10 from 2013.
Fwiw - Half were in the batting lineup most of the time. Half rarely hit.
Aces who hit -
Oklahoma – Keilani Ricketts (122 AB, .369, 12 HR)
Alabama – Jackie Traina (117 AB, .333, 13 HR)
Washington – Kaitlin Ingelsby (178 AB, .354, team-leading 12 HR)
Nebraska – Tatum Edwards (140 AB, .286, 11 HR)
Michigan – Sara Driesenga (134 AB, .246)
Aces who didn't hit -
Tennessee – Ivy Renfroe (1 at-bat)
Florida – Hannah Rogers (2 at-bats; #2 pitcher Hager batted .319 w/ 18 HR)
Arizona State – Dallas Escobedo (Did not bat)
Oregon – Jessica Moore (34 AB, .206)
Texas – Blaire Luna (Can’t find, but don’t think she hit)
Fwiw - Half were in the batting lineup most of the time. Half rarely hit.
Aces who hit -
Oklahoma – Keilani Ricketts (122 AB, .369, 12 HR)
Alabama – Jackie Traina (117 AB, .333, 13 HR)
Washington – Kaitlin Ingelsby (178 AB, .354, team-leading 12 HR)
Nebraska – Tatum Edwards (140 AB, .286, 11 HR)
Michigan – Sara Driesenga (134 AB, .246)
Aces who didn't hit -
Tennessee – Ivy Renfroe (1 at-bat)
Florida – Hannah Rogers (2 at-bats; #2 pitcher Hager batted .319 w/ 18 HR)
Arizona State – Dallas Escobedo (Did not bat)
Oregon – Jessica Moore (34 AB, .206)
Texas – Blaire Luna (Can’t find, but don’t think she hit)