Is this possible?

[moog]

...just make sure they all get grouped invited the same every time.

I use the jamba command "/jamba-team invite" to group up, as that invites my chars in the order that the team is defined in the Jamba team screen, waiting for each char to join before inviting the next, so you always get the group in the same order.

The ISBoxer "Invite Others" keymap invites the other chars but doesn't wait for #2 to join before inviting #3, so, depending on client response time, you can end up with a random order.

[MiRai]

I use the jamba command "/jamba-team invite" to group up, as that invites my chars in the order that the team is defined in the Jamba team screen, waiting for each char to join before inviting the next, so you always get the group in the same order.

The ISBoxer "Invite Others" keymap invites the other chars but doesn't wait for #2 to join before inviting #3, so, depending on client response time, you can end up with a random order.

As far as I know (I haven't used the default bars in years) is that it puts your portrait at the top of the party.
So if you're on Character01's screen he is on top of the displayed list. Then, if you move to Character02's
screen, he is on top of the displayed list which would mean Character01 is now in a different position than his
own screen essentially jumbling up the order. This all happens regardless of the order you invite your
characters and that is why people use unitframe add-ons with the ability to sort the order. Again, I haven't
used the default bars in years and something could have possibly changed, but I have a feeling it hasn't.