On Vista and later (under Aero), it shouldn't affect performance too much since the OS uses compositing anyway and it is optimized for this (which is why Microsoft recommends a graphics card for running Vista). On XP, it definitely slows things down because it wasn't designed with full-fledged alpha compositing in mind.
By per-pixel alpha, do you mean that you want parts of your window to be transparent? If yes, DirectX won't help you at all - DirectX will only help in rendering transparent images onto your window's background, but won't make your window itself transparent.
