Having a small radius instead of a sharp corner does not add much strength but it can make an enormous difference to fatigue resistance, especially in the case of aluminum and its alloys which will eventually fail due to fatigue when they experience a reversing or cyclic load.
Is this applicable to the bottom of pockets? That depends on how the part is stressed. If the part is a load bearing part where the pockets are for the purpose of reducing weight then probably corner radii are a good idea. Actually for some parts they are essential; think 'wing spars' on aircraft.
Small radii at the bottom of counterbores for bolts are probably a good idea especially if the part is highly stressed in a cyclic manner.
Radii are also a good idea at any abrupt changes in thickness because a sharp corner here can create a region of raised stress that may exceed the failure strength of the metal under a bending load; even when the average or distributed stress is well below the failure limit. This is a situation where a radius can inprove strength.
Because it can be slower machining pockets with a corner radius mill you have to use your judgement, or get advice from the designer of the part, as to whether a radius is wise, or essential, in a particular area. Certainly if you are making pockets that form the internal cavities in some sor of high pressure hydraulic or pneumatic manifold radii are probably going to be needed. In this case they should be called out in the drawing or model and omitting them is a bit irresposible.
An open mind is a virtue...so long as all the common sense has not leaked out.