Yes, you can upgrade your server at any time.  However, keep in mind that most upgrades will require taking the server offline and out of the rack to perform the upgrade, meaning you will experience some downtime.  Some upgrades, like adding RAM or an extra hard drive, can be done more quickly and would not require much time out of the rack, while other upgrades, like upgrading to larger hard drives, would require more time to perform.

On some servers, the processor can also be upgraded if desired.