With a career .312/.379/.536 line in more than 2,300 minor-league plate appearances, it's not out of the realm of possibility for him to perform like a poor man's Travis Hafner for a few seasons.
However, the 26-year-old first baseman has at least one obstacle between himself and playing every day for the Royals at Kauffman Stadium. That obstacle is Eric Hosmer, who has a stranglehold on the corner position for the foreseeable future.
Barring injuries to a series of players, Robinson's best chance to play for the Royals is as a bat off the bench. He would probably play well in that capacity for manager Ned Yost, and certainly would provide more value than a 12th pitcher or a speed-only reserve such as Chris Getz. While Robinson's only tool at the major league level would probably be power, his left-handed bat would be valuable if the club needed to pinch-hit for a righty late in a game.
The Royals are running out of time to find out how Robinson would play in the majors, as he could be a six-year minor league free agent after the 2012 season. Robinson's window of opportunity might only arrive once he departs the organization for another willing to let him compete for a job off the bench.