I've flown from abroad to JFK three times this year (holding a non-US passport) and the time to clear immigration has been extremely variable: >5 minutes, 50 minutes, 1.5 hours. The time depends basically on you outrunning the people in your own plane and your luck on not having other planes arriving just before yours (of course if one is sent to secondary screening, then it's a completely different story and we would be talking of hours).

In all cases (even the under 5 minute one), my bag was already going around in the carousel when I got there, so not checking bags wouldn't have helped. Clearing customs and rechecking your bags usually take just a minute or two.

Finally, take into account that you need to go through security again after rechecking your bags which can take 15 minutes or so.