That is possible but clearly you have to modify the source code. Basically you can modify the code to periodically retrieve information from a server and perform actions accordingly. In fact, the firmware already has a component, namely the NTP sync, which is similar to what you want to do: it periodically retrieves the current time from an NTP server.
Alternatively, you may want to check out the OpenSprinkler Pi, which has a demo program that makes use of the Google Calendar for scheduling sprinkler events. It’s a polling-based method, and the