No, some boot loaders like Windows' rely on the boot flag, because it simply passes control to the partition boot sector.
But Grub does not require this; it knows which partition contains additional grub modules and the config file and loads them based on that information rather than the presence or absence of a boot flag.
If you run the bootinfoscript it will tell you more information about your system, including where Grub loads it's files from. Usually Grub will locate this partition based on its UUID, so modifying other partitions doesn't affect booting. But if Grub is booting with the partition number, deleting or adding partitions may result in boot problems.
I would recommend having an Ubuntu bootable USB available so that you can reinstall Grub if required.
Q. How does the BIOS know it should run Grub?
For BIOS based (not EFI) computers, BIOS looks to the MBR (master boot record) to find the main bootloader and partition table. This is where Grub is installed (or the windows boot loader). The problem with this is that the space is very limited so the functionality of the bootloader is too. For Windows' bootloader that's okay because it does little more than pass on control, but Grub takes a different approach and loads up additional modules as required directly from it's /boot
partition.
If you look at the results of the bootinfoscript it tells you what is installed in the MBR as in:
============================= Boot Info Summary: ===============================
=> Windows is installed in the MBR of /dev/sda.
or
=> Grub2 (v1.99) is installed in the MBR of /dev/sda and looks at sector 1 of
the same hard drive for core.img. core.img is at this location and looks
for (,msdos5)/boot/grub on this drive.