Grub is still the first bootloader in that case. You would not notice if it was putting itself first after an update unless you have Windows booting first.
You might notice if you are booting between multiple linuxes, all with their own version of grub.
Again, unless something has gone wrong, the grub config should auto-detect the other Linux distros installed and add them to the boot menu. It should look like this:
EDIT: Also, what can happen is that the grub timeout (the time that menu is on screen) is set to 0 seconds. You can get the grub menu to stay up by holding left shift during boot if that’s the case.