On my hardware, (GeForce 9 9800 GT, Intel Core 2 Duo, 2GB RAM), after disabling it LO runs really faster and snappier. A new feeling when using it now.
The hardware acceleration checkbox applies to Impress slideshows only - and there, depending on your operating system and display drivers, running w/o it might indeed boost performance (or degrade it) - it’s simply excercising different code paths in your graphics subsystem.
For most cases, though, having this enabled yields faster & nicer results.
The hardware acceleration (which is on by default) does not work with a Dell XPS13 laptop.
It causes the slideshow screen to be completely messed up (either with builtin display
or an external screen through a DA20 adapter). Disable hardware acceleration and it works fine.
Richard