Question about the google extension add-on

I would like to know if the google extension would help me solve the following issue.
I’m using the EA to book one-on-one call support.
I have installed it on my main site (mysite.com) targeting the public; and on a subdomain (kb.mysite.com) which targets my clients. I would like to somehow sync both installations so the time slots/availability match both calendars.

My question is, if I sync both installations to the same google calendar, can the “two way option” keep both installations updated?
e.g.: mysite.com book a time slot —> it syncs to G calendar –> G calendar syncs back with kb.mysite.com and update the time slot.

Please let me know if this is possible.

Thanks.