Is it possible to get dysphonia from advair?

Yes: Topical steroid inhalers are a notorious cause of dysphonia (hoarseness), topical steroids over a moderate period of time may cause swelling and injury to the vocal fold mucosa. Sometimes it may be permanent. But if a topical steroid inhaler is necessary for your asthma, then you have to accept this side effect.

Yes: I've seen this a number of times. It is the steroid component that does it. It usually goes away with stopping the medication, although not always.