Will that increase reservoir pressure? (unlikely, at least in the time it takes to do humans any good).
If a stratified reservoir which was produced too rapidly re-stratifies (the cone-ins level out), that might appear as if it has recharged but actually, there isn't any new oil to speak of, it is simply rearranged in respect to existing well bores.
I an an engineer but have worked a lot around geologists and I now appreciate the wondrous world of geologic time which is something to behold.