There are very few medications that are compatible with flying that will cause a false positive on DAMP. Pseudoephedrine/“Sudafed” is the famous one - but the argument has always been that if you need to take it, you are probably taking it to mask symptoms that are incompatible with flying, so you should be staying home anyway.
If you are uncertain, your employer does not need to be your source of advice. Most would seek their advice from a third party (GP/DAME/CASA).
So, no, you do not need to disclose your medications to your employer, unless, as you point out, you are taking something that happens to be compatible with flying that contains a testable substance - which is unlikely. Otherwise, it is your responsibility to turn up fit for work and with nothing in your system that will cause a DAMP positive. How you achieve that is up to you.
Your heart medications, anti-cholesterol, blood thinners, anti-anxiety/anti-depressants, sleeping tablets, birth control, and arthritis medications have nothing to do with your employment relationship, and can stay safely between you and your GP, DAME, and CASA.
There is a good reason for this, and it is that is why it is enshrined in law.
So this comes back to the original question of whether an unscrupulous employer can mis-use your IHI to discover your medical history (which they have no right to, and there are penalties if they are caught).