Yes, it will, although the bootmenu is then gone, so you'd better have some way of booting to reinstall the bootmenu.

And if you want to update both SD and flash, the best routine seems to be

1. Boot to SD
2. Update
3. When it reboots, it'll come to flash (because no bootmenu)
4. Update
5. When it reboots, it'll come to flash again
6. Install bootmenu.
7. On reboot, you'll have options as expected...

However, my setup is more complicated than that, and I use Fanoush's package independently, so I'm unable to say I've done exactly that.