Yes and No
It depends on what you mean by Detected. Allow me to elaborate:
Stealth aircraft (F22, F117, B2 etc.) still have a Radar cross-section. That is, they are not invisible to Radar. They are about the size of a Bumble Bee (reportedly, this is not the War Thunder forums...).
And as such, most Radar systems filter them out - after all, think of how many birds, Bees and other things that might cause a Radar return in the sky that are the size of a Bumble Bee - you would have so many targets that the system (both human and computer) would break down and cry.
Why all this guff about Radar - well, if you have big long afterburning flames, you need to fly high enough so that these are not visible from the ground (probably around 10,000 ft or higher) - which means you are going to be visible to Radar.
Furthermore, since it is New York (and therefore densely populated) you cant do any form of low-level terrain following flying to hide yourself from Radar.
So, you are going to be tagged by Radar.
A regular human has an approximate Radar cross-section of around 1m².
Aerial Missiles (which are detectable on Radar - but we will get to that) are around 0.1m².
Wikipedia defines a Stealth Aircraft as something with a Radar cross section of less than 0.1m² - Ideally we want to be about the same Radar cross section as a Bird or smaller (0.01m²).
However - things like Distance and Radar type are also a factor in detection. A Commercial Radar setup at say JFK international are not going to be setup to track something as small and fast as an Aerial Missile (let us for the sake of argument assume the Radar array can, it is just not configured to do so).
So, our goal should be to minimize the Radar cross section to be small enough that it is filtered out by most Radar systems.
A suit made out of Radar Absorbent Material (RAM) - I think is feasible enough, something like the paint used on the SR-71 Blackbird, or some special mesh material that absorbs Radar waves instead of reflecting back.
This should allow us to get small enough on Radar that most systems wont notice us.
However - unless he constructs a special suit with angled surfaces (like the F117), I think he is still going to have enough of a return that a modern fighter jet (like the F22) in close-ish proximity, could probably detect him - but the chance that there is going to be an F22 intercepting him as he is flying is small - but it is a risk.
In short - I think it is plausible that with a relatively simple suit, your villain could reduce their Radar cross section to be small enough to be ignored by most commercial and ground-based military Radar installations - but if he gets close enough to a modern fighter, he might have problems.