Most people these days sign up for websites at where they live rather than on public/work computers. So, on forms that require the user to enter their address, should they be filled in by default with their current location?
No, this shouldn't be default. You could offer it as an option but I wouldn't give the user too much choices because of reasons already mentioned (false data). And not ever user is happy when websites try to get their location automatically because of privacy concerns - although they can turn location off, of course.
I would only offer this option if the location is really helpful for executing the users' task (eg. travel planners, public transport planners).