It isn't likely. An NBA caliber player that is a senior will likely have played 100+ NCAA basketball games. A few good/bad games in the tournament isn't going to change their overall chance of getting picked in the NBA draft. And the NBA draft is very shallow to begin with, only 60 picks total and still some of those players don't make the teams. In the NFL and MLB it is very common for undrafted/late round picks to become stars, but not common at all in the NBA where your physical ability (which is easily measurable) is so important for excelling.
There also is the G-League which is essentially the NBA minor league. Anybody on the bubble of making the NBA who wants a job will get a chance in the G-League, and if they were truly NBA caliber then they'd prove themself and get the opportunity.