Question: If the applicant checked into the hotel (Reservation made by program manager), and authorization was given on the document (by the DH), but the comptroller had not yet obligated the document at time of check in, is that an UAC? When discovered, funding document was obligated within 2 hours of checkin.
My opinion, absolutely not.
As defined at FAR 1.602-3(a) an "Unauthorized commitment, as used in this subsection, means an agreement that is not binding solely because the Government representative who made it lacked the authority to enter into that agreement on behalf of the Government." None of that appears to have happened in this instance.
Maybe you meant to ask if this was an Anti-Deficiency Act violation. Instead of explaining what that is here (because we answer similar questions too often here at AAP) you can use our search feature, which is fantastic, to read some of them; just type GPC and anti-deficiency in the search block. Or you can read this great, short article on "Anti-Deficiency" You will see that typically those do not occur at a micro, tactical level. Your organization clearly had the funds (the right amount and the right type), there was just a short delay in getting them obligated.
Taking a step back, let's interject a little common sense here. The federal procurement system standard is reasonableness, not 100% perfection. You have hard working people trying to do the right thing, get the mission accomplished, and not purposely evading proper policy or procedures, especially for personal gain. This is nothing more than a clerical issue and timing mistake due to internal procedures, no violation of procurement or fiscal law tenets appears to have happened in your scenario.