Why does Professional Edition allow viewing Managed Package Permission Sets & assigning them to Users?
Are there any Permissions that can be set in a Permission Set that affect a User's Permissions in Professional Edition?
When we made the decision to allow permission sets in professional edition, it was to follow a similar model to profiles:
To answer your original question, if you mean user permissions like Modify All Data, no, it's not possible to affect user permissions with permission sets. The reason for this is that user permissions are not supported with packaging - for instance, it's not possible for an ISV to assign Modify All Data in a permission set that they package with their other metadata and you install as a subscriber. It's also not possible for an ISV to add access to standard object or field permissions in a packaged permission set which could otherwise have an impact on user permissions.
However, if you mean a user's permissions like CRUD to a packaged object or field, then yes, by assigning that packaged permission set to a user in professional edition, that user will now have access to that ISV's field or object. Since this is limited to what an ISV can add - it should protect you from inadvertently affecting any user's access to non-package metadata.
To see an example of what is possible from what is not with regards to permission sets in professional edition, check out the following blog posting: http://www.salesforcehacker.com/2013/05/whered-that-field-go-installing.html.
Hope this helps...
From the ISV Force Guide page titled Features Available in Group and Professional Editions, permission sets aren't available for use by managed packages in the Professional Edition. You'll note that custom profiles are also not available in that edition either.