Yes, maybe and it depends: as long as the VNC client is connected to the server, the client must accept and process any data sent by the server. The reason is that RFB protocol is not framed so the client must process everything sent by the server or it will lose track of where it is in the data stream. However, the largest chunk of data that is sent from a server to a client is frame buffer updates. Generally (but not always) these are sent in response to a frame buffer update request from the client. Some clients may stop sending the periodic frame buffer requests when minimized (but that would be client dependent so you would probably need to crack open the code to find out). But not all data is in response to client requests (i.e. DesktopSize, Bell, SetColourMapEntries, ServerCutText, etc), so the client can't stop processing data when minimized.
Also, stackoverflow is for programming questions. You were probably voted down because your question isn't really programming related. In the future try and at least give your question a programming spin to it. For example, "I'm thinking of implementing a VNC client..."