I see that Merriam Webster (no pun intended) also has web as a verb:http://www.merriam-webster.com/dictionary/web...
I must confess I have never seen it in nearly 40 years as an English native speaker (and language professional).
And, in any case, I think "to web" means "to use a web", not to build one.
Just like "to club" someone doesn't involve making the club first ;-)
Have a look at this nice forum about spiders:http://www.arachnoboards.com/ab/archive/index...
A spider is described as having "webbed" something:
"She's in a small tank but she has webbed it up and eaten, so I think she'll be okay."
That kind of usage sounds fine to my (UK) ears.