Yes, just be sure to specify that you are requesting a transfer and NOT a new domain. 

You should keep the service with your current provider while waiting for the Registrar to complete the transfer process. We will provide you with a temporary ftp address so you can upload the site on our server. All email and web pages will still be accessed from your current site. 

When the Registrar announces the completion of the transfer there is a 24-72 hour propagation period where visitors could go to either site. At the end of the 72 hours you should contact your previous host to have them delete the old domain from their records and update their DNS record. If you use this same provider for your Internet access you will not be able to access your domain site at Cyberspace until they update their DNS.