Ben29, in your sketch's plan view, I would not expect a void like you show to cause a problem. There should be plenty of bearing area between the footing and the underpinning. I would not expect the bearing of the existing footing to cause more than about 20 to 40 psi (about 3000 to 6000 psf) bearing - very low for concrete compression stress. Even if you discount half of the bearing area due to a possible void, you may be talking 40 to 80 psi (6000 to 12000 psf) bearing on concrete. A small void probably will not matter. If a big void is present, the odds are the drill holes will find it.
EDIT: The entire, top surface of the underpinning pier should be leveled off using a flat 2x4 so that you know there is at least 1.5 inches available to ram in the drypack. Ideally, there should be a 2.5 to 3 inch, or more, gap between the top of the underpinning pier concrete and the entire bottom of the existing foundation being underpinned. Pouring the underpinning concrete up against the bottom of the footing, even with some extra head,
MIGHT provide full and proper bearing but also
MIGHT NOT and is also hard to confirm.
bookowski, I have designed underpinning in NYC where everyone, especially DOB, expects to see shims, wedges, permanent jacks, etc. It is my experience that shims, wedges, jacks, etc. are rarely, if ever, needed. Proper dry packing will evenly transfer and distribute the building load to the underpinning. Wedges, shims, and jacking can cause high, possibly damaging, load concentrations on the existing footing, especially if it is a rubble stone foundation wall. NYC DOB has previously questioned me about my non-specification of wedges and shims and has accepted my explanations. (Of course, I probably just jinxed myself for my next underpinning project.) My clients and I have designed and built underpinning projects in many different northeast and mid-Atlantic states and have never used wedges, shims, or jacks unless needed to temporarily support some loose stones in a foundation wall until the pier is ready to be dry packed.