"Can you have an asthma attack with a normal sat reading"? The answer is..YES!
While it's a little unusual to see a person with a perfect O2 sat of a 100% during a severe exacerbation, its pretty typical to see sats in the 94-97% range. The reason for this, is that asthma is a disease of the airways , not the alveoli where gas exchange takes place. Most asthmatics dont desaturate during the early stages of an attack,unless theres a secondary problem such as pneumonia. You have to be extremely ill with asthma if your sats are low.