Before the season started, I would have said yes. Now that Reitsma is positioning himself as a "somewhat steady" closer, I would say it looks less likely this season.
However, Street got the job last season because Dotel went under the knife. I don't see Reitsma having Tommy John (he doesn't throw that hard) but the moment we have any injury to the Braves bullpen, he's the first to come up. Even so, I don't see him taking the closer role unless Reitsma really screws the pooch (or gets hurt).