Can the login to my Windows computer also log me into my IP phone?
It is not trivial to do but it is possible – it requires custom programming. Assuming the Windows computers are in a domain, you would use the login script in Windows netlogin to trigger it or if not, local login file that is defined in your user records in Windows -- that is the easy part.
Next you would create a VB script or a program in most any Windows languages to generate AMI commands to log you into phone passing login information. The password for the phone would need to be something generated from login username – extnumber and macid or something like that because there is no possible way to get the password used to login to Windows and pass that anywhere else, it is encrypted and impossible to reverse encrypt, it is a security thing in Windows.