Can you collect a resource of your choice if you have no production due to the robber?
From the original Catan rules:


  Important: If the production number for the hex containing the robber
  is rolled, the owners of adjacent settlements and cities do not
  receive resources. The robber prevents it.


I think it's clear from that that a player doesn't receive production in the scenario that you outline, even if production in some sense occurs.  

As such, you should be able to collect a resource of your choice from your improvement.