The clamp will definitely help prevent any wear and tear on the connector from cable weight or the cable accidentally being pulled. But it's not going to prevent issues that come from constant plugging/unplugging. Unfortunately, HDMI connectors are not really made for repeated use like that, so you can run into issues with connectors over time if you are plugging and unplugging cables often.
You may want to try one of the HDMI adapters that are also compatible with the BMPCC cages. That way you can leave the adapter plugged into the camera and just plug/unplug your HDMI cable from the adapter. Then, if a connector wears out it will be on a fairly inexpensive adapter or cable instead of the camera body.
Tilta makes an adapter that fits their cage:
Tilta Full Cage for BMPCC 4K/6K
Tilta 90 Degree HDMI Adapter
While a lot of reviews state that the adapter doesn't fit the Tilta cages, I have not found that to be true. I had that same Tilta cage for my BMPCC 4K and the 90 degree HDMI adapter fit perfectly.
And SmallRig makes one that fits the same cage I mentioned earlier:
SmallRig HDMI & USB-C Adapter