We currently have Network Solutions as our domain registrar. We are looking to transfer the domain to 1and1. We use Office365 to handle our email and other hosted services, so the only change we made to Network Solutions DNS settings was to set the nameserver to Microsoft's nameserver (Microsoft, in turn, created a handful of CNAME, A, and MX records for our actual website, Sharepoint, and hosted Exchange server).
Will we be able to complete the transfer without any downtime (particularly to our email)? I think we should be able to, because the nameserver will still be pointed to Microsoft's and we aren't changing any DNS settings. We are simply changing which registrar we use for our domain.