That works OK until you hit a site that has a weird method of processing payments, and now you can't pay for your order from email+weirdsite@mail.com because your paypal address is email+paypal@mail.com and they have to "match" (and ofc you had no way of knowing this before signing up). Or the sites that don't think "+" is a valid email address character. Or the sites that strip out the "+blabla" because they've decided they're too special for filtering.

Will that automatically archive them?

And besides, many sites that are necessary for doing business think luke+priceline@somewhere.com is an invalid email address. (And all of Priceline's competitors agree, and Kayak/Hipmunk are meta-search engines so don't solve the problem.)

That said, Priceline does allow you to unsubscribe from their marketing and only receive relevant emails, which is probably the ideal place to attack this problem.