The amount of recoverable oil probably will not be affected. That's having to do with long term pressure loss of the reservoir with gross volume of fluid removed. That's independent of pump rate, since it quickly becomes limited by permeability of reservoir rock and "geologically" slow inflow from reservoir to the production zone. You will dry out the production zone until the reservoir flow into the production zone can equalize with the pump out rate at some increasing radius (as you begin pumping from the well) where reservoir pressure is constant.
You may observe some recovery of pressure near the well in the shorter term, if a well remains offline, as for a well recharge test. Plotting pressure and recharge time and flow and pressure VS time on a subsequent flow test can give some indications of the surrounding geological structure, if you are able to read those. I cannot, except for knowing when it's not circular inflow.
This recharge rate is set by how fast fluid in the surrounding reservoir (where pressure can be considered as constant reservoir pressure, like i said above.) can flow into the production zone and make its way to the wellbore, of which permeability and reservoir pressure are most important. Since the pressure drop near the well is logarithmic, assuming radial flow, the distance to the effectively constant pressure reservoir interface isn't all that far. (probably eventually reaching a max 1500 ft?, but depends on permeability, oil viscosity etc. ). That area may experience some recharge which can be pumped out at a faster rate until you once again reach equalization with the flow rate across the reservoir to production zone interface. Any increase in rate is thus usually temporary. Comparison with previous recharge and flow rate tests may suggest changes have occurred during a long shutdown and perhaps some needed maintenance activities to do.
So, no, no increase in long term producable oil. There may be more of a chance for less oil as permeability may suffer with no flow, oil sticking to sand, water accumulations, flow channels collapsing and other effects such as debrie in the surrounding rock may have been carried by oil flow to the well zone which dropped out when flow was stopped. Hard to say what could happen.