Yes, if someone steals your private key, then he can make a fake server with the same name, and users won't see anything wrong with it (provided the attacker redirects connections to his server, e.g. by altering the DNS).
No, users will not be warned.
From the point of view of both the CA and the user browser, a fake server with a stolen key is not different from a Web server being moved to another IP address, e.g. as part of a DNS-based load balancing. When you have a server and a certificate, the certificate is in no way locked to whatever IP address you presently used; browsers only check that the server name appears in the certificate (see RFC 2818, section 3.1). You are free to copy your private key and certificates to another server with another IP address, and make the DNS point to that new address. The only difference with the attack scenario you describe (key theft) is that this time you really want it. Whether you agree to the IP move or not cannot be checked by the client, and, correspondingly, the client does not check it in any way.
So protect your private key, and, if it gets stolen, report the theft to your CA which will then revoke the certificate.