Not sure if Haiku OS will work in a triple setup, but I did a setup with ArcaOS, Linux Mint and Windows 8.1 a while ago.
Using the ArcaOS utilities to partition the hard drive went well for ArcaOS and Windows, but the Linux Mint installer (installed last) didn't want to let me use the previously made partition for Linux because "it is not properly aligned to HDD boundaries".
So I let it re-create the partition, installed Linux Mint, and then went back to ArcaOS maintenance mode and "corrected" the partition errors.
Everything works, everything boots.
And yes.. if your Linux distribution lets you install no boot manager at all, it would be for the best.
This is because installing grub onto the linux partition, you will see two boot managers at start:
1) start the machine
2) first AirBoot wants to know what to boot
3) if you select "Linux Mint", AirBoot boots directly into GRUB, where you can choose again. (makes little to less sense)
So.. would be best if Air Boot boots Linux directly without using GRUB at all.