Yes, I believe you can. There are also other inhaled steroid treatments that leave the teeth and gums vulnerable to disease. Thankfully, when I was rx'd years ago with an inhalant tx. for asthma, I was also advised to Always Brush My Teeth after using them.
Thrush is not always an STD ~ it's also known as Candida Albicans, which is a yeast imbalance in the system; women are especially vulnerable to yeast imbalances and we can carry them in our bodies for long periods of time ~ with no symptoms.
So, not to worry ~ go to the dr. if you can/need to ~ but there are plenty of home remedies available for thrush/candida if you're willing to treat them aggressively.
If you have insurance, the medical and rx treatment will cost less. Anti-biotic tx. will also kill the good bacteria that we need in our bodies so just be sure you keep your system balanced out with fresh Acidophilus to keep the yeast in "proper balance".
Best Wishes ~ LZ
Here is a site with info on advair... go down to side effects.
http://www.drugs.com/advair.html