Regardless of when it closes, smart buyers will know about this property. IF you listed yours a and IF it went into escrow sometime before that property closes, chances are you will not get through escrow without the other property showing up either as sold or back on the market.
I would based when I list on other factors, such as its readiness to show, the existing competition on the MLS for comparable properties, and the local state of the market. Sicne you are purchasing another before selling this one, I assume that you would be able to hold on and keep it as a rental if all else fails.
Otherwsie, I would have sold first then purchased.
SDL does not show listing, but zillow does (removed sept 4).