Technically under the present rules I think it can happen but it would probably be a creative interpretation.
If the FIS aerodrome is in Class D, then it's in Class D - whether in the ATZ or not is not going to change the airspace class. Consequently all flights are subject to ATC clearance from the controlling authority - this will be the ATC unit and not the FISO by definition.
If everyone involved was minded to make it happen I think what would have to happen is that a defined portion of airspace around the FIS aerodrome would have to be set aside for the aerodrome's use. Within that airspace there would have to be a 'standing' clearance for VFR flights to take place with appropriate buffers built into the FIS aerodrome airspace to ensure that the traffic information passed by the ATC unit is adequate.
A couple of potential stumbling blocks.... You might find that some take the view that each flight at the FIS aerodrome should be subject to an individual clearance - but I think there are plenty of precedents where things take place in a portion of a CTZ without an individual clearance.
Maybe more problematic is the issue of responsibilities. The ATC unit is going to be responsible for the services within the airspace assigned to it - including the FIS at the remote aerodrome. From a legal perspective consider who will carry the liability if the FISO provides inaccurate or incorrect information (please note that I am not suggesting that a FISO is likely to do this for any reason but we're all human) - it's quite possible that the ATC unit may be considered to be ultimately responsible for the ATS in the airspace. The procedures and resources and the like that would be necessary to offload this liability would probably be significant and unless it offers a benefit to the ATC provider there would be little incentive for them to go to the trouble.
I'm not aware of anywhere which has such an arrangement but it's more likely somewhere where the same ANSP provides the service at both aerodromes. There certainly have been discussions about plans to downgrade some ATC units in Spain to FIS so you might find something similar to the situation that interests you down there.
Don't forget that within 18 months the way in which airspace is established and operated falls within EASA's competence and so you may find the rules change - although that doesn't mean for the better if past experience is anything to go by!
Drop me a PM if you've got any questions about what might be required by the CAA and so on - I have a bit of experience that might be of relevance, albeit it's a few years ago.