Type Rating + ATP
Yes, if you have ATP written exam complete and meet the part 61 requirements for the ATP, the practical test results in an ATP certificate with the A-320 Type Rating - there is no difference in the check since they both come from the ATP and Type Rating Practical Test Standard (PTS).
HPA has good reputation but was allegedly taking shortcuts on type rating checkride - FAA intervened but not sure what happened in the end on that one.