Yes there is a certain sense of accomplishment when you receive your invitation to join a glo. However...maintaining good status and climbing the status ladder (i.e. getting positions on the executive council) is not an automatic thing. It takes a lot of work and effort to get there. I'd say, take the automatic in...if you think the guys are a good match for you. From there,work to make a difference in the group and challenge yourself to grow as a person (get leadership experience).
Let us know what happens.
in_the_zone
P.S. I wrote this thinking you were considering going for TKE. I then realized you may already be affiliated. Consider my post for what its worth in any case