On my A1200 the CF is very quick. You are limited to the ~2MB/sec of the IDE port on the A1200 motherboard. What makes it quick is there is no seek time to speak of on a CF card, so it boots up in no time. My workbench is ready before my monitor has warmed up enough to display the image if I do a cold start.
Once in Workbench, it definitely "feels" a lot faster when accessing files and folders, however if you are going to copy a lot of files or large files, it will still take a while due to the 2MB/sec limit of the IDE port.
Just a warning if you do get an accelerator for your A1200, some CF cards don't initialise in time when you cold boot the A1200. It'll give you the insert floppy screen. Usually a Ctrl + A + A will allow it to boot, but it is irritating when it doesn't want to boot first time.
My Transcend 4GB and 8GB 133x cards boot fine on an accelerated A1200 but my Trancend 16GB 133x card won't cold boot, I have to Ctrl + A + A to get it to boot.
Unfortunately I don't have an A4000, so I don't know if it'll show the same symptoms of the A1200, especially as you have such a fast accelerator for it.