Hah, no. I don't even know why that adapter has a female A on it; the only thing it would work with is the equally silly A-to-A cable.
Besides, it has a 5-pin mini-B on it. I have those - I've made those! It's the connector I wish was used by the keyboard. But the keyboard uses the old style 4-pin mini-B which is physically completely different.
Hence the need for another cable jammed in my bag *only* for the keyboard.
(I did try replacing the socket... but opening the keyboard is practically impossible and almost certainly a self-destructive event. Gah, why glue when the thing's also perfectly well screwed together!?)