As long as you're being careful then it should be okay...I've been doing the neck bends for about three years, but I've found a few other ways too.
I only literally push the guitar and neck when I want a little sort of...shimmer to go through the note, never a crazy half step/full step thing like he did at the end there. For those sorts of things I'd use my strumming hand to bend the string above the fret I'm sustaining, ala Randy Rhoads. Or I push the string behind the nut, ala Tony Iommi. Or I push the string down at the bridge/stop bar ala John Sykes.