There are a few things that you should be aware of.
1. If you are administratively reduced? That is considered an "administrative action", meaning it is no judicial (like a court martial
further, it is also considered non punitive. So it is not like Art 15 which is punitive.
So the reduction is not, in and of itself, going to impact your discharge, other than to change the rank at which you are discharge (assuming the reduction takes effect pursuant to the board).
It will not impact the characterization of your discharge (so if nothing else happens, you will get an honorable discharge)
HOWEVER, the administration reduction does not prevent other judicial or other non judicial action. So, for example, the commander could, independent of the administrative reduction, seek to process you for administrative separation under AFI 36-3208 for the misconduct. If they go this route they could try and give you a "general" discharge or an "other than honorable" conditions discharge.
Now...they have to give you notice, in writing, before they can separate you...and with your contact almost over (2 weeks left) unless they move very quickly they are not going to be able to separate you for the misconduct. In order to separate administratively you and give you a less than honorable discharge they must give you notice, in writing and the chance to respond.
If they have not done this yet? It may be it never happens.
But to answer your question, COULD this incident (the DUI) impact your discharge characterization? It could...but again, only if the command acts quickly.
Also, I will say it would be unusual for a command to go to the effort of administrative reduction if the plan was to administratively separate. That would not make much sense, since if the Airman is administratively separated for misconduct, there is an automatic reduction to E3. So I doubt it will happen in your case, but it possible, at least in theory