No, you can't obtain that information from the Data Explorer. The PostWithDeleted table was only added to allow reporting over trends in tags, closing, deletes, etc., not as a means to gain easy access to deleted content or its authors.
If the post was created more than three months ago (and not yet deleted at that time) you could fetch the Posts.xml from the datadump and find the id of the post you're interested in. That record will give you all content, including the owneruserid.
An alternative might be the Internet Archive Wayback machine, but they don't capture all pages.
You'll need the Access To Moderator Tools privilege that comes at 10K (2K on beta sites) of reputation to see a specific deleted post. Either get that reputation on the site the post is on or maybe ask in chat if a user with said privilege is willing to help you out.
Let me add a warning for casual readers: Not all users appreciate being randomly contacted about their posts and that might be even more so for deleted posts. Keep that in mind once you managed to find the userid and now want to take a next step...