You only really need a shaker grate if you are burning rice coal, which is the type used in modern coal furnaces (it is, inexplicably, rice sized). If you are looking to burn some in your woodstove, you'll want to get nut coal which is pieces ranging from striker marble to tangerine size.
Is the coal you can get in Utah bituminous (sometimes called bit coal or brown coal or soft coal) or anthracite (aka hard coal)? I would avoid bit coal as it smells and is smokey... anthracite burns very clean and hot.
As for the suitability of the stove, I'm not sure what to tell you other than that coal can burn VERY hot. Also, you will want to be able to control the draw with some precision in order to control the burn rate and heat, especially in order to cool the burn if it is getting too hot. You'll also want to make sure that your chimney is up to the task of handling the increased heat.
Last but definitely not least, get a CO detector if you don't have one already. Coal has a somewhat deserved bad reputation of burning anaerobically in stoves with a tight draw, which can lead to CO generation.
If you are looking for more info there are some threads over on the hearth.com forums.
Good luck!
-Grant, great-grandson of a blacksmith