Yes you can do it. Make sure that transparency is on using SetObjectTransparency(). Then use SetObjectColor(object, r, g, b, a) and change the alpha value. Unlike sprites, you can't change just a single colour at a time so you have to use a type to hold object ID and colour information and set all colours at once. I usually have something like this:
type PlayerUnit
UnitObject as integer
Red as integer
Green as integer
Blue as integer
Alpha as integer
endtype
dim units[16] as PlayerUnit
function Fadeout(unitID)
if units[unitID].Alpha > 0
units[unitID].Alpha = units[unitID].Alpha - 1
SetObjectColour(units[unitID].UnitObject, units[unitID].Red, units[unitID].Green, units[unitID].Blue, units[unitID].Alpha)
endif
endfunction