Anything that impacts the passage of air through your nose will impact your study results. This includes colds, allergies, deviated septum, polyps, etc.
To answer directly, having congestion will impact your results. It is possible you could see an increase in the number of flow limitations which could be flagged as RERA's. Enough RERA's and you get tagged w/ having UARS.
Plus having a cold likely means you won't sleep well anyway, or at least restfully.
It is worth a call to your doc to get their opinion. My advice is to make them back up whatever they say. In other words, don't trust them to have your best interest at heart. If they say it won't impact the results, ask them why not. If they say it will, ask them why.
You can google 'allergic rhinitis and sleep' to find information on nasal congestion and sleep. There are plenty of research publications. You can extrapolate from there regarding colds/congestion.