Yes, photosynthesis will take place, but there will also be metabolic activity taking place in response to the wounding that occurred in excising the piece of leaf. The smaller the piece, the greater the area of wounded tissue relative to the intact volume. Punching out a disc minimizes this for a given size. So, if you are using this method to estimate intact leaf photosynthesis, you will need to account for this side effect. There are undoubtedly published protocols for washing leaf disks to minimize the effects of wounding.
It´s not problem. I recommend you to buy very accurate oxygen electrode. I have bad experiences with Clark type electrode. It needs often calibration and change of membrane. Also I recomend simultaneous measure of fluorescence. Good luck.