I have wargamed Wagram a couple of times and IMHO it indeed is possible for Charles to win.
Charles victory at Aspern just before was a shock to the world - Napoleon wasn't invincible went out the cry.
If he is also defeated at Wagram the effect of course will be manyfold, but it must not be forgotten that France still had a very dominant position in Europe. Austria is unlikely to change that alone, but may be aided by either internal French strides and/or by other European powers joining another coalition against France. The first is IMHO unlikely, Napoleon was firm in the saddel until the enemy litterally stood before Paris and after an entire Grand Army had been lost in Russia. The second option is more likely, but may take some time to carry out. After all Russia was a kind of French ally and Prussia was in no position yet to enter the ring.
But Austria is most likely going to end up after 1809 in a much more favourable position, even if Napoleon decide to continue the war and manage a comeback victory. Even if this happens the Austrian/Habsburg position in the coming battle over the "German soul" will be much better vs. Prussia, and the German Empire, WWI and II as we know them suddenly vanish.
If the Austrian success in 1809 is overwhelming (like because Napoleon falls) I could be worried the Habsburg revanchism in Germany would be too harsh to ensure stability.