Highly unlikely. In fact, it would be a stunner if they did it, considering how they have approached the five other player arrests in the past 13 months (wide receiver Robby Anderson, outside linebacker Dylan Donahue, and cornerback Rashard Robinson). All of those guys remain on the roster. Donahue was popped for two DWIs over that span, too. He recently completed an alcohol rehab program. Anderson was also arrested twice.
With Austin Seferian-Jenkins leaving for the Jaguars in free agency, Herndon was (and probably still is) expected to compete for the Jets' starting tight end job with Jordan Leggett, who missed his entire rookie season last year with a knee injury.