It would be fairly easy to do. You'd need several inbound DIDs (phone numbers) for patients to call. Each DID would be routed to the voicemail system (*98) which would prompt for the mailbox number and password.
The only trick would be creating sufficient extensions to support the maximum number of concurrent messages you need to distribute. For example, if you have 200 patient test results active at one time, you'd probably want 300 extensions.
To populate the messages, the staff person would call the mailbox to be used, delete the old message, and add the new one.
In creating the extensions, you would want different passwords for each extension, and this password could be handed out with the extension number to the patient when the test was performed. Whether to change the extension voicemail passwords periodically would be up to you.
With a programmer, much of this including password changes could be automated. Then the application could be licensed to other physicians.
We do some projects like this under the following terms. We own the software. You make an up front contribution of $2,000. You get a license to use the software in your practice when it is complete. Assuming the package was priced at $100 per system license, we then would reimburse you $50 on each subsequent license sale until your entire original investment is recovered. We then get rich off the continuing sales.

That's the theory anyway.