As a matter of fact, investigating pooling pressure and mining centralization threats in bitcoin I've become convinced that an affirmative approach to the above question is inevitable in the framework of any solid solution to the core problem of mining centralization.
I don't see how paying full nodes some sort of reward for running could have any effects on mining and mining pools. That just adds an additional reason to centralized another aspect of bitcoin (running a full node) and if we assume there were any centralization in mining the same entities would also run full nodes and take the control in that area also.