ANYTHING will kill a deer under certain circumstances. Missouri just legalized the "atlatl", a stone age spear.
The spread of circumstances under which a certain caliber,round, or weapon system will kill becomes much smaller until the practicality of use as a hunting platform is negated.
I've engaged in arguments about the capability of the .223 Rem as a deer hunting tool many times w/o much success so I suppose the .204 will be the next "fools' endeavor" for this use.
In answer to the specific question, yes the .204 will kil a deer. Would it be a good choice as a deer hunting tool=NO. It is designed for and uses bullets designed for varmints. There are so many better options that using such a cartridge is just foolish.