Here is a HostGator article which explains how to avoid downtime.
What about my Database?
If you are concerned about your databases staying up-to-date, all you need to do is disable your databases so that they cannot update while we complete the transfer. We require up to 72 hours for all transfer requests. The time will depend on how large is your transfer. (If you need the content transferred faster, you may transfer the files yourself.)
After the transfer, you can create an A record to redirect all visitors to the new server; this is much faster than waiting for the propagation of new name servers.
You can also configure your site to connect to your new database, remotely; this way whether your visitors are directed to the new site or the old site, all the new updates will be saved to the new database. Now the new database will have all of your current information and can continue to update.
Also, after the site transfer, you can create a MX record so your emails will all be delivered to the new server and not need to wait as long for propagation.