Catan: play development card after rolling robber
No, you can’t do that.
Under the rules for rolling a 7, it says that you “immediately” move the robber. This implies that cannot do anything in between.

a) Rolling a “7” and activating the robber



If you roll a “7,” no one receives any resources.




Instead, every player who has 8 or more resource cards must select half (rounded down) of their resource cards and return them to the bank.




Then you must move the robber. Proceed as follows:





(1) You must move the robber immediately to the number token of any other terrain hex or to the desert hex.