Short answer:
#No.
No.
Long answer:
#Noooooooooooooooooooooooooooo.
Noooooooooooooooooooooooooooo.
please don't try to keep users on your website unless you have a very good reason to. Saving form fields would be an example of a good use. Checking if they're moving on to another website would be a bad use.
People don't travel from page-to-page as much as they did in the early days of the web. Instead they use google and social networks to find interesting pages, and consume separate distinct pieces of information.
