Do they usually test for alcohol in a urine test?

This depends on the test performed.

"Dracula" may want a sample too :-)

Urine is a normally good indicator of a lot of different drugs, but some drugs dont show up here. Some drugs even break down into various breakdown components that is sort of normal, but if levels are high, the good doctor may "play Dracula" in order to find out if your blood contain illegal substances