The Rawlings Professional Unfinished Birch Wood Baseball Bat: RABIRXXX are random models when purchased as this bat can be any one of Rawlings turn models. All bats, regardless of which one is received, will be Major League quality birch wood so it does not surprise us to hear you received a bat with the pro ink dot test on it.
No, these bats will not have an ink dot on them because they were pulled from the production line before finished construction. These are blemished bats that are still good quality, but did not finish construction and are not labeled as a specific turn model.
Although it is noted that these bats are great options for "batting practice or cage hitting", these Rawlings Professional Unfinished Birch Wood Baseball Bat (RABIRXXX) would certainly function well as a game bat.