I started to post on this several times over the last few weeks, but I keep hoping you would get someone who knew more about these particular plants in your particular area.
Hasn't happened.

You're leaving the tubers in the ground to keep going after the aboveground parts have been cut down, and harvesting tubers over the fall/winter/spring? Then this whole idea should work, I think.....

The clover will fix nitrogen and shade the ground under the sunchokes in a hot climate. This should help the seasonal aboveground growth of the sunchoke plants. As long as you let the chokes really die back til they look brown and scruffy, and don't just cut them down when they stop looking 'pretty', they should send all the good stuff into the production of the tubers. The clover might actually increase rather than decrease the size of the tubers.

If you're gradually harvesting the tubers over a couple of months, rather than hard-digging the whole patch at one time, then the clover should recoup nicely.

Part of my problem with this is that, in my area, I cringe and quake at the idea of planting white clover among vegetables..... But I live in Michigan, not Georgia. Big difference.

I live in South Carolina & have no problem with the hot sun in my climate, for sun chokes.
But still like the ideal of a green cover that will fix nitrogen to the soil. White tail deer may be a problem with clover.
So please post what you have done & how it is working for you in Ga.