If the 4020 has rear PTO and sleeve hitch/3 pt hitch then yes your tiller should work nicely.
Exceptions would be any belt driven attachments like the snowblower or mower deck as these are required to spin the opposite direction on the 3000/4000 series. There was a conversion kit available to convert the older snowblowers to work with the newer tractors but the mower decks are not compatible.