Define 'thickish piece of plate'? Unless the plate is at least as thick, (assuming the plate is steel, much thicker if any softer material is used), as the diameter of the bolt being screwed into it you will not have a strong fixing as there will be too few threads in the plate, see
HERE for minimum thicknesses for different diameter bolts. A sheet metal 'Nutsert' or 'Rivnut' might be a better option if the plate is not thick enough...