NATO has responded pretty variably to the 9/11 attacks that prompted NATO help over our skies (and then in Afghanistan). The same would apply if Turkey calls on NATO help:
If Turkey goes to war with Syria, expect NATO to make a similar contribution. Turkey has already shown restraint in responding to Syrian provocations, so is unlikely to mount a full-on ground invasion of its neighbour. An air campaign, perhaps with limited ground actions, is more likely. NATO could play a role in such an effort by sending early warning and command-and-control planes, search and rescue assets, naval patrol vessels and providing Turkey with additional munitions, should it run low. NATO could provide electronic and satellite intelligence to Turkish military officials. And if Turkey needed help with its air campaign, perhaps NATO (read: American) warships and aircraft could knock out some Syrian air defence batteries with long-range missile attacks.
That sounds about right. Each NATO member can decide how to respond to their obligations. In the Cold War, it was safely assumed that the Red Army plunging west into the heart of Germany would result in maximum efforts by everyone but France.
Now, without that obvious threat, the issue just isn't clear.