The answer to your question depends on your body and to some extend your age and the type of infection you have.  Younger people have a tendency to heal quicker.  I have seen asthmatics as you describe recouperate in a few days, and I've seen some who've been admitted to the hospital take 5-7 days or longer to fully recouperate.  It just depends.

Perhaps your doctor will have a more specific answer for you, yet I would "assume" he'd give you the run around the same way I just did as there really is no way of knowing for sure.  However, you doctor does know you better than we do.

You may want to note that any lung infection can trigger asthma.  Likewise, Advair usually takes 2-3 weeks to fully get into your system, and therefore is recommended mainly as a preventative medicine than as a medicine used to treat acute asthma episodes. 

Yet Advair is a medicine that can make your lungs stronger and better able to deal with any lung infection you might get in the future. It also creates more receptor sites for your Albuterol inhaler (I'm assuming that's what the "blue inhaler is") and makes it work better.   It is for this reason you may want to discuss with your physician staying on Advair even when you are doing well so the next time you are hit with an infection it doesn't make you feel so bad.