I had it sleep for 5 seconds and it appears to be working now? Why wouldn't WinWait work?
Code now:
Func AdAware_Install()
Local $path = "\\***.***.42.137\programs$\PC\AdAware\Adaware SE Personal V1.06.exe"
Run($path)
Sleep(5000)
WinWait( "Ad-Aware SE Personal", "")
ControlClick ( "Ad-Aware SE Personal", "", "Button1" )
EndFunc