I know that extracellular calcium can replenish intracellular calcium stores. However, they myriad of papers on the issue appear to be contradictory as to the requirement for extracellular calcium in phagocytic cells.
Not sure why you need to maintain macrophages in EGTA for 12 hrs and whether this would be at 37° or 4°C. If at 37° C, then it is highly likely that cell injury will occur since cell metabolism, respiration and ATPase function will likely be inhibited in the absence of calcium and magnesium (as Dr. Wong mentioned, EGTA is not specific for calcium). If at 4°C, then this treatment will probably have much less of an effect on macrophage function, but some effects are still possible.