Disagree based on following:
1) JM's "looking included" did not help him score earlier in the night, and his actions are not of insecurity, so doubt it would be a motivator for him
2) She was probably thirsty after the walk (whether she was ready for another beer is really difficult to know.)
3) Nobody remembers them both going in (albeit, nobody remembers JM going in the second time.)
4) HG is under age and would not get past the ID checker (She didn't get into McGrady's earlier either.)
4) The action of buying 2 drinks and paying immediately is a finite move, get and go. If he was going to try to shmooze/seduce/drink her into submission at a table, maybe he would have left the tab open, or ordered antoher round of drinks after 1:10.
5) The chances are much higher they would have been seen if hanging together at a table, and it sounds like he stood out like a sore thumb.
6) Both of them were active and fast moving leading up to that, so sitting at a discreet table (if such exists) would be a contrast.
IMO he went into Tempo because it was right there (closest bar on their trajectory?). He knew it inside and out. Not cheap, but convenient.
All this to me says it is more likely than not that he got drinks while she waited outside for 2 minutes, he brought them outside under his shirt, then they drank them on Water St. or in a parking garage or the alley back there since open drinks are not legal on the street. The ID girl only saw them when the came back around the corner and headed up Fifth St.
Ultimately, it doesn't really matter whether they were inside, except to Tempo and except for solving a part of the mystery of HG. The more significant events took place later.
However, it could mean there is some evidence back in that alley. I now remember reading a bloodhound got a hit in a "parking garage on Water St." so I will go back and look at the possible proximity. Water and 4th or Water and 5th stands out to me for some reason.