Does it? I know it was supposed to but it didn't/didn't work. KB888111 can not be added to a machine that already has had SP3 installed as an update, because it (KB888111) looks for SP1 or SP2. However even after installing just SP3, HDA is still not installed. There is a modified patch on the net, that can be used on a SP3 machine, that will install MS UAA, but it doesn't come directly from Microsoft. The alternative way, is to uninstall SP3, install KB888111, then reinstall SP3.
Slipstreaming SP3, I did not think would make a difference as to KB888111 installing after the fact. I can report though that having both installed into an image does indeed install the UAA, and Sound is available. It has been awhile, but I am pretty certain that just slipstreaming SP3, did not get the UAA installed.
The method if slipstreaming patches I use is
WindowsXP-KB936021-x86-ENU.exe" /integrate:"C:\CDImages\XPCD"