I've taken my Dahon onto PATH trains during rush hour, and have used the PATH for many years as my daily commute. Most of the following comments don't apply to NJ Transit.

Folding bikes during rush hour are allowed on PATH and I haven't had any problems. The conductors won't let you take a bike on the first (conductor) car, although I have yet to see any actual written rule for that.

I don't recommend taking a standard folder on PATH trains during rush hour as part of your daily commute, though. The PATH trains are crowded, and even as a folding bike rider I would not be thrilled to routinely bump into an unbagged folded bike morning and evening. The bike still takes up a lot of space, gets dirty and is somewhat inconvenient both for you and your fellow passengers. Almost all the PATH stations only have stairs, and lugging a Boardwalk up and down those stairs (and around your fellow passengers and over the turnstiles) 5 days a week will suck, especially if you bring work clothes or other stuff with you.

If you must do it, either take the ferry (expensive) or go early (when there's fewer people) or get something smaller and lighter (e.g. a Brompton) or greaseless (e.g. a Strida). Unless you go greaseless, get a bag; if you take a bike on the PATH every day, it's inevitable that one of your fellow passengers will get dirty from your bike, and unpleasantness will ensue.

NJ Transit still means stairs, but has overhead racks and does not have turnstiles. I think NJT + Brompton / 16" wheels is far, far more feasible than PATH + 20".