Isolating GPIO's using diodes
Besides Petre's analysis, think about this for a moment. If your circuit would work, your R1 would be 'strong' enough (value low enough) to pull 4 GPIO's low. If that were the case, you could use 4 resistors with a value four times as high, to achieve te same effect.

In most cases the very small current through pull-up reistors is not enough to warrant special attention. But if it is, an appropriate trick is to enable the resistors only during the (relatively short) time you want to read the switches. This can be done using one extra GPIO. Or use the internal pull-ups of your micro-controller, which can (in all cases I am aware of) be enabled and disabled under SW control.