No. Laboratory equipment can differentiate between concentration (called a specific gravity) and drugs. And some tests only require 10ml of urine to run, so not having enough urine wouldn't do it either.
If you failed a drug test, you had enough of one of the drugs being tested for in the assay to test positive. Be aware, certain tests also test for things like nicotine, diuretics, and other prescription medications. If you are legally prescribed a medication that would show up on a drug test (i.e. Narcotics, ADD medications, anxiety medications, muscle relaxers) you may fail the test unless you can prove you were prescribed the medication.
Also, even if you live in a state that has legalized marijuana, companies don't have to allow it. You can be fired for using marijuana even with a prescription. You can also be prohibited from smoking or other tobacco usage.