To the best of my knowledge, counterfeit detector pens test the paper, not the ink content, so it should be fine.
Ah, I found a link:
The relevant info:
The counterfeit detector pen is extremely simple. It contains an iodine solution that reacts with the starch in wood-based paper to create a black stain. When the solution is applied to the fiber-based paper used in real bills, no discoloration occurs. The pen does nothing but detect bills printed on normal copier paper instead of the fine papers used by the U.S. Treasury.
There are many other hidden anti-copying features hidden in US currency-- microprinting, embedded strips that respond to UV light, special inks, and more. It’s fascinating stuff!