Let's first understand that we want a layer that moisture cannot easily/rapidly penetrate.  Commercial woodwind bore oil is often simply a particular viscosity of mineral oil.  This is a simple hydrocarbon (paraffin) mixture like common motor oil. It is rather incompatible with wood and only coats the very surface.  It basically never dries and seems to loose its effect after several weeks. Oils which are biologically derived from natural sources (i.e., almond, tung or linseed) may be slightly more "soluble" in wood, but when spread out in a thin layer, will cross-link and "dry".   These oils tend to last longer after application. Paraffin waxes or biological waxes are just higher molecular weight versions of petroleum and biological oils, respectively. My advice would be that commercial bore oil won't hurt and can be applied once or twice a year.  I oil my pipes in the spring and fall.

Another reason for oiling the bores is to help smooth the surface of the bore.  A rough bore acts like a filter to remove some of the harmonics of the sound. In general, smoother bores have more high frequency content in their harmonics. Polishing or oiling results in a smoother bore and increases the fraction of high frequencies coming out of the drone. Depending upon your point of view, this may or may not be a good thing!   Some pipes have the reputation for having gun-barrel-smooth bores and do not require oiling.

A rough bore also presents more surface area for absorption of moisture from your breath into the wood.  Rough surfaces have more surface area and, therefore, take up moisture faster and potentially result in a more rapid build-up of stress. If the rate of moisture uptake is slowed sufficiently to allow equilibration of the moisture level between the wood on the inside and outside of the drone, the wood will not build up stress and will not crack. Once the wood is equilibrated to a humidified level and the drone is played regularly, the moisture level in the wood will not change and the drone will not split.

The roughness of the bore can be treated by either oiling or polishing. Oil or wax creates a water-resistant layer that slows the uptake of water into the wood, it also fills in the imperfections in the wood surface making the surface smoother. Polishing reduces the surface area available for absorption of moisture and thus keeps the rate low. Both techniques will reduce moisture uptake. Both approaches will alter the sound of the drones.

The decision to oil or not is ultimately yours to make.