The main question is if Sept and the Q2 adjusting period are both open.
If I post an entry to Sept and run translations for the Q2 Adjusting period will Sept translations be updated too?
If not and I run translations only against sept will the ending balance in the Q2 adjusting period be updated with the new balance?

Adjusting period is just another period. There is nothing special about it other than it spans only one day (usually 31-DEC which could overlap other period).
Lets say you have two periods: period 1 and period 2.
If you enter and post a journal in period 1, the PTD balances in period 1 will be affected (for the accounts used in the journal). PTD (period to date) balances of period 2 will not be changed.
However, YTD (year to date) balances for period 1 and all subsequent periods (including period 2) will be affected.
If you enter and post a journal in period 2, the PTD balances in period 2 will be affected (for the accounts used in the journal). PTD (period to date) balances of period 1 will not be changed.
Also the YTD (year to date) balances for period 2 and all subsequent periods will be affected. YTD balances of period 1 will not be changed. Hope this helps.