Looks a few years old and it was a fairly dated way of doing things then. In short though you’ll want to setup a staging area so you can test it on a php7 environment for all the major functionality (membership areas and signups).
It’s really quick to setup a staging site if you have ssh access to the server and mysql or some kind of database access.. it’d be hard to say without trying it as you don’t know what Christmas tree lights will turn on!
I’ve done some pretty horrific migrations before on sites much larger so I wouldn’t be put off – you’ll probably get an idea if it’s plain sailing or a nightmare in a couple of hours.
Does look like your site is overdue an upgrade to a responsive site with some more modern practises. I’d probably take that opportunity to move over to a CMS like wordpress so you can get away from Contribute 😉