Can asthma drugs affect my baby if I'm pregnant?

Yes but... The likelihood of harm from not taking the drugs (asthma attacks) is much more likely than the risk of harm from the drugs themselves, and the risks tend to be minimal at the worst. Stay on your asthma drugs, talk to your physicians about your concerns, and follow their individual advise for you (much better than internet generated general advise).
Generally No. We think that current asthma medications are safe for the baby. You need to check with your doctor for advice specific to the medication. But remember, asthma is not a healthy state for your body. In a severe attack your body may not get enough oxygen and build up unhealthy toxins. These conditions may seriously hurt the baby. The medicines ar the much safer option!