In principle, yes he could escape. As you can see in the scan below (from Uncanny X-Men #445) Nightcrawler has the ability to teleport away from things that are touching him. If he was trapped in a sticky web, it would be a simple matter to teleporting a few feet to the left and the web (which isn't part of him) would remain in place.
Per Marvel's description of his powers:
Nightcrawler is a mutant who can teleport by opening a portal into
another dimension, travelling through it via an unconscious
direction-finding sense, and returning to his own dimension
Through practice, Nightcrawler has increased the mass he can teleport
with him, though the limit to the amount of weight he can carry when
teleporting and the distance over which he can teleport with such
additional loads are unknown.
If, on the other hand Spiderman was able to obscure Nightcrawler's vision with a dense enough web, that would be a different matter:
Nightcrawler has a limited unconscious extrasensory ability that
prevents him from teleporting into any area that he cannot see
As you can see from the scans below, Spiderman has attempted to catch Nightcrawler in a web on at least one occasion. Although we don't see his escape a frame later, I think we can reasonably assume he used his teleportation powers given that there's no web visible on his outfit (as there would be had Wolverine used his claws to cut him free).