Chances are, without some InfoEngine task running in the background, probably not. I've always wanted to pull simple things like Revision out of Windchill and append to a title block using a Pre-Update hook for my schematics and layouts. I can do the actions required on the CAD side of things (for me, that's Cadence), but simlple things like the revision number are not exposed to the hooks.
My suggestion would be to write a custom pre-update hook to see what information is available to you (write a set command in the hook file, to post all system variables available during the hook execution). If the info that you want from your Windchill object is in there, then you just have to write additional lines to add that information to your Altium design, before it gets updated.
If you need help with the hooks, check out CS131522 for example hook files.