Most CMOS batteries are the CR2032 lithium button cell type batteries and are not rechargeable. There are rechargeable batteries (e.g. ML2032 – rechargeable) that are the same size, but they can’t be charged by your computer. Some motherboards used to have rechargeable CMOS batteries on them but they seemed to stop I assume due to cost cutting by the manufacturers.
In a completely sane world, madness is the only freedom (J.G.Ballard).