They could if they made people sign up via an external site which logs IPs but sadly most campaigns don't care about alts even though the majority of them prohibit it.
Wait, is that actually possible?
Yes, of course. You don't even need to create your own website. Even simple online form apps like
TypeForm capture user IPs to identify a duplicate. They don't disclose the actual IP addresses though, instead, they will give you a
Network ID which is a unique string linked to IP addresses (i.e. same IP address will have the same Network ID).
You can use the form as a registration form for your signature campaign enrollment and capture participant IPs. It may not be failproof though, but it is extremely simple and easy to use. If you want more personalized and detailed info about user info I guess you need to create your own website or search for a website that is more focused on IP logging.