You don't have to be paranoid to know that running a virtual machine is not "hiding" anything. You just have to understand how networking works.
When you connect to a local area network via Wi-Fi or ethernet, for example, it is trivial for the network owner to know that your box is there. You can't simultaneously use the connection AND be "invisible". Adding a virtual machine does absolutely nothing to change that. If nothing else, you'll be detected at the physical layer, or the link layer, even if your box emits no packets and ignores all inbound packets.
Even if you had a wide open ethernet hub that you wanted to sniff packets on by just passively listening to the traffic, the hub would become "aware" of your connection as soon as you establish the physical and link layer connections. You can't simultaneously connect and not be detected.
Also, I usually assume good faith, but the short and pointed nature of this question sounds like you are trying to do something illegal like steal someone else's Wi-Fi. I see no reason to help you do that.