Yes, one of the Miner Health criteria is Fuel, which is another name for your mined MXC.
If you remove your mined MXC from Fuel (e.g. moving it to your MXC wallet, staking it, withdrawing it, etc.), this will impact your Miner Health, which will then reduce your MXC performance by up to 80% (if all the mined MXC is removed).
There is currently a 90-day "grace period" (after setting up your miner), in which your performance will not be impacted by Health and Fuel. After the grace period is over, your Health and Fuel will start to impact your performance.
So to keep your performance maximised from day 91 onwards, we recommend keeping your Health and Fuel as high as possible.