Yes, you can. To avoid downtime while transferring your hosting account to us you will need to do the following:
1. The first step will be ordering one of our hosting packages which suits your requirements.
2. Do not cancel your previous hosting account!
3. Once your package is active and you receive your Welcome email, upload your content to our server.
4. Once the content is uploaded, re-point nameservers to the ones indicated in your Welcome email.
5. As a result, your domain will be resolved to your previous host from the places where the propagation has not been completed yet and to a new one, from the places where it has already passed.
6. Once the propagation is finished all over the world, you may delete the content on your old hosting.