I'd guess: no, not in a quality you can show anyone. In PEG you have a lot of etheric carbon which will probably dominate the C1s signal as well as the ether oxygen that will dominate the O1s signal. So, the carboxyl will already be a minor species in the spectrum and you will only be able to isolate that by component fitting. Ester vs. COOH will then be a "subcomponent of the minor component" analysis which you can try but I doubt that this fit will result in publication-quality data. I mean, XPS fits are already difficult to handle for a reviewer and the deeper you go the more probable it will be that someone will reject the analysis.
Thats what I thought too but I dont have any XPS experience, I wanted to make sure. I know IR will help to identify the bonds but ll not be able to quantify it. With titration I can find the total COOH but the one that are only available on the surface.