Hi!
As far as I know, they should work fine together. By default the search results page override is not activated in Ajax Search Pro, so it simply redirects to the results page when hittin the return button – where the items should be overridden by SearchWP, if it’s activated.
I’m not too familiar with the SearchWP plugin in depth, but as far as I know, it automatically overwrites the search results with it’s own, when visiting the results page.