Can I legally display my foreign license if pulled over in the USA if I already have USA license?

In New York State, you can legally drive using your foreign drivers license and the state does not require that you carry an International Driving Permit. That you retain your NY license becomes coincidental, as you would no longer be considered a resident. That may become an issue when renewing, but that's off topic.

Should you be stopped, and present your foreign license, the police will run your name in their in-vehicle computer. The first search will be in the DMV database, which has information on where you 'live,' your driving record, and, in some states, your biometrics, including a photo. Other databases that may accessed during a traffic stop reveal any outstanding arrest warrants and criminal history, either in local police records or the Federal National Crime Information Center.

So the answer is, yes, you can show only your non-US driving license. Doing so might avoid repercussions on the sole occasion. However, a record will be created of the offense against the license you present. If the officer does not connect you to your DMV-issued license, you got lucky. If/when the connection to your State-issued license is made... well then, you know the rest.