Alveolar-arterial PO2 difference (A-a)PO2 breathing 100% oxygen

    Would the alveolar-arterial PO2 difference (A-a)PO2 be normal in a healthy person breathing 100% oxygen; i.e., would alveolar and arterial PO2 both increase by the same amount?

No, the (A-a)PO2 will be greatly increased in healthy lungs breathing 100% O2.  
The figure below shows inspired to venous blood partial pressures during O2 breathing at 1 ATA (100% O2 at sea level). In this example, it is assumed that all nitrogen, argon and other trace gasses have been washed out of the system. During O2 breathing, the ventilation/perfusion inequalities in lung have a much greater impact on PaO2 than during air breathing. Under optimal conditions during O2 breathing at 1 ATA, PaO2 would be about 500 mmHg while alveolar PO2 is about 663 mm Hg. (PAO2 = (760 - 47) - 40/.8 = 663). As blood moves through tissue, the same 4.5 mL O2/dL blood is extracted, and PO2 falls to 57 mmHg in venous blood. 

A look at the oxyhemoglobin dissociation curve helps explain why the (A-a)PO2 difference is so high. Because of the flat upper portion of the curve, a small drop in O2 content due to normal shunts and low V/Q cause a large drop in PO₂ (from PAO₂ = 663 to PaO₂ = 500 mm Hg.