Hello from JustAnswer.
Yes, they can test the urine to determine what drugs you are taking, but no, it is not typically done. They may do testing to look for drugs of abuse, but they typically would not perform drug testing to look for psychotropic medicines beyond those that may be abused recreationally.
Almost every drug is metabolized into a form that can be detected in the urine, but they will typically not be interested in testing for the 1000s of different drugs that are available. If it were to be done, they would be able to determine which drug is being taken. There are screening tests for certain classes of drugs that will only determine that a drug within that class is present, but advanced testing can determine which drug is actually present.
The only time that there would be difficulty in identifying the specific drug is when the drug that is taken is metabolized into another drug. For example, Vyvanse is metabolized into dextroamphetamine, both of which can be used for ADHD. Testing would not be able to differentiate between someone taking Vyvanse form someone taking dextroamphetamine. For the drugs that you are taking, though, this would not be an issue.
If they were to test for Seroquel, it would common;y be detectable for about 5-7 days.
There are tests that can be done to determine whether it is urine from a male or female, but these tests also are usually not done.
In summary, then, since you ask whether they can test for these drugs, the answer is yes, this is not typically done, so there is no reason for you to be concerned about them testing for these drugs.
If I can provide any further information, please let me know.