Yes—leave the normal plastic lens cap on if you want the extra physical protection. A standard plastic lens cap is mainly there to protect the front element from scratches, bumps, and dust; it is not an airtight seal. Because of that, it generally will not reduce the effectiveness of a dry box or dry cabinet or meaningfully trap moisture.

So for typical storage, cap on or cap off should make little difference to humidity control inside the cabinet. Keeping it on is usually fine and gives the lens some protection.

The only caveat from the community answer is that this may be different with unusual storage setups, such as certain metal caps or other accessories, but for a normal plastic lens cap there is no real concern.