Writing to serial if nobody listens?

Hi, I want to add to my project the option to be connected to the internet. I'm able to communicate with my router running openwrt, over the serial connection. So far so good.

I want to make the internet connectivity just an optional feature. If the router in not connected to the arduino serial, and the sketch is still writing to the serial, would that be a problem? What happens when the serial buffer is full?

TIA

I don't think it would be a problem. The Rx/Tx pins will do what they think is transmitting the data, and nothing will happen.