Maybe.
The airplane would have to meet several special requirements to operate in the IFR system, under an IFR flight plan. You'll need to so some research. An LSA cannot operate in IMC, but that's OK since you want to do hood/safety pilot flying.
Can you log hood time while not actually on an IFR flight plan, ie practice approaches? I don't see why not, assuming the airplane has the minimum required instruments for IFR operations. If you log hood/SP time in a cub or LSA which has only a wet compass and slip/skid, the FAA might not see the humor in that.