A question about heart disease - specifically Hypertrophic cardiomyopathy

Yes, an insufficient amount of blood could enter the heart and an insufficient amount would be pumped out. She could also get an attack of arrhythmia with the same effect.

After passing out, her heart would probably beat faster, because she was running before that, and because the lower heart output would result in a drop of the blood pressure and reflexive increase of the heart rate. It's basically the same mechanism when you pass out from, for example, heat or strong emotion....In case of an arrhythmia the heart rate could be anything from slow to very fast, and the rhythm could be irregular.

The doctor would listen the heart using a stethoscope. She could get an intravenous injection of a beta-blocker, or an anti-arrhythmic drug. Beta blockers slow down the heart rate enabling the heart to fill with the blood and expel it properly. If she was taking beta-blockers before, she might need no drugs at all, like you usually need no drugs when you faint. They would tell her to keep lying down for, let's say, 30 minutes and they would offer her something to drink (a herbal tea, for example).

An easy to read article:
http://www.patient.co.uk/health/Cardiomyopathy-Hypertrophic.htm
A detailed cardiologist-level article:
http://emedicine.medscape.com/article/152913-overview