Do I have to skip saving to the server when using mock-data?

I'm quite new to the whole unit-testing thing. I wanted to look into all this things about mocking, got a slight idea how it works right now.

In my application, I send objects to a server via a webservice to store them there. If I do the same thing with mock-objects instead of real objects, do I still have to send those objects to the server? The only reason I see to do this is that I can also test the connection to the server. Would it be correct if I just skip the whole "saving to the server" part?

Thanks in advance