coppers fine with conductonaut. Aluminum however is a big no no as it will effectively eat it away in no time.
You won't see much of a difference to be fair and it isn't really the correct TIM to use between IHS and cooler due to the problems with increased risk of spillage + thus shortage and a dead board and or CPU.
Conductonaut is best with things like GPU-cooler. Or when a CPU is delidded. Its not worth it on IHS to cooler, due to transfer issues. As there is a lot of metal and paste to transfer the heat through, CPU-TIM-IHS-TIM-Cooler.
Enough to mean that a good quality paste vs conductonaut is going to be a few degrees either way. Conductonaut is best on nice flat surfaces with a thin film and an IHS can be all over and are usually quite concave.
Not worth the risk in my opinion. Just swap back to something like grizzy kryonaut.