I have looked for an official support position on this and not having any luck. I have a machine with Office 2013 Click-to-Run installed as part of the Office 365 Home Premium offering. This offering does not include Visio.
I have a separate Visio 2013 retail license for a local installation. I would like to use that on the same machine as the Office 2013 Click-to-Run installation.
In the past, I have had issues doing this with a CTR copy of Outlook with a local install of Lync, but that's a special combination given the Lync-Outlook integration so I don't think I can apply that experience here.
This is different than the case of preview vs. release as both products are not preview versions (there's another question that relates to the Visio/Office 365 combination but it explicitly relates to that combination after starting with Preview, so it doesn't directly apply here.)
I know Visio is available as an Office 365 licensed product with CTR but that would mean paying for another copy of Visio, if that offering is even available in combination with the Home Premium O365 SKU.
What I'm looking for is someone who has done this kind of setup - O365 without Visio and local Visio - confirming it works, giving hints, explaining any support issues, etc.