I wouldn't test that the machine is online. I would just do what I want to do and handle the error that occurs when disconnected.
The only case I can think of where there might be an advantage to testing is if there is a lot of work to prepare for whatever transaction is to happen over the network. Even in this case, I think a better solution than testing would be to do the work and use the results immediately if the network connection succeeds or save them to be used later if the network connection fails. In this way, the work of preparation is done only once and there are no superfluous tests to give false negatives or false positive.