Place a signup form on a sub-site which registers the user on the main site?

Is there a way to place a registration form onto a sub-site which then registers the user on the main site?

What I want to do, is have the user register on the main site, then use the User Synchronization plugin to add the user to each of the sub-sites. I'm thinking this will solve the problem of users being unable to register on the site because they registered on another, and getting confused.

The sites are all for a similar thing, online book tours, so people will be wanting to register on a number of the sites, and this should make things simpler.

Also, is there a way to do it so that if a user is already logged in to one site, they will be shown to be logged in on other sites too.