Will the adapter enable screen sharing from Intel Mac to Mac mini?

Yes that should work as a dummy HDMI display in the Mac mini instead of a real display.

Only problem I see, is that you may initially need to connect an HDMI TV or a display to the Mac mini, so that you can turn on and setup Screen Sharing.

see > Share the screen of another Mac

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If I may ask, why do you want to access the M4 Mac mini from the old 2013 Mac Pro...?

When the M4 Mac mini can take several displays and run circles around the old 2013 Mac Pro.

FWIW I would connect my best display(s) to the M4 Mac mini and access the 2013 Mac Pro using Screen and File Sharing.

FWIW, you will still be limited by the performance of your network. While the device unlocks graphics capabilities to be available via the network, the fact that you will be running multiples of these sending screen video over the network along with all the normal traffic across the network, the performance could be underwhelming depending on what your actual use is.

If your use case is to simply peak at the Minis to see what is going on with them you may be fine. Anything else may have poorly performing video and end up need to knock down the resolutions to get something useful.

Macrules34 wrote:

I expect to have to have a display (and keyboard and mouse) connected when doing the initial setup (not a problem).

👍

The reason for using the 2013 Mac Pro is because that’s how I have it setup currently, I can change that but don’t see the need.

Again, the M4 Mac mini can run circles around the 2013 Mac Pro and it's time to sell or recycle the old 2013 Mac Pro.

If you don't believe what I'm saying, compare the benchmarks.

https://browser.geekbench.com/mac-benchmarks

You're welcome.