Its not possible at the moment because individual member wager totals are not tracked/stored in the xf_user table (only Sportsbook Event Counts for bookies are), so there is nothing to base a conditional off of at the point of rendering (as content is fetched via AJAX when clicking on a tab). The next version will display a message stating that the user currently does not have any visible content to display.
I had a need to track counts for wagers, so I've added a new field to the xf_user table 'sportsbook_wager_count' which stores the total amount of wagers a user has placed.
With that said, I can now use that data as a conditional on the TM (template modification) that adds the "Recent Wagers" tab to the member profile. The "Recent Wagers" tab will no only ever display IF the member has made any wagers.