lol, no it's not. That would be very scary, Apple just accessing your voicemail without any compliance from your carrier. That would be highly illegal.
Yes, it is.
Apple is not accessing your voicemail in any way. If you choose to use Live Voicemail, everything is handled on device.
When you use Live Voicemail, the caller hears your chosen Siri voice tell them to state why they’re calling and that the other person might pick up, then Siri records and transcribes the caller, and if you don’t pick up, it’s saved to the device itself. If you choose to reject the call entirely, bypassing Live Voicemail, then it goes to your carrier’s voicemail system.
The two do not sync; Live Voicemails are not available on your carrier’s system, and carrier voicemails are not part of the Live Voicemail system.