Yes, you will win.
And a ruling on exile:
No, "In play" is the old wording of "on the battlefield". Suspended cards aren't on the battlefield. They are found in the exile zone, so they do not prevent the ability from triggering or resolving.
The ability checks the following two zones: The battlefield and your hand. Cards in libraries, in graveyards, on the stack, in the ante zone, in the command zone or in other players' hand do not prevent the ability from triggering or resolving.
You can even win with BG on the turn a suspended card "unsuspends". Simply place the suspended card's triggered ability on the stack first and BG's triggered ability on the stack second. BG's triggered ability will resolve before you have a chance to cast the suspended card.