Definitively yes - I do it all the time. Most multifuel burners are optimised for an under draught (suck air beneath the grate) to prevent the grate warping. Wood fires do not get hot enough to over heat the grate and burn better on embers (which fall through a grate) so better quality makers supply a different type of grate for wood (e.g. Esse) but wood will burn fine on a coal grate - just not quite as efficiently. You should not however burn coal in a stove designed only for wood as coal gets much hotter and can warp or crack the stove - I have seen several cast iron stoves damaged in this way
Hope that helps
Red