Hi Sonia,
TECO status in a work order symbolize the Maintenance Task/Work is completed, but you can do settlement / MIRO... Refer below link to have deeper understanding
Difference Between TECO & Business Completion
Invoice posting might take time for the finance to perform it, also there are lot of process involved from Finance prespective. Since we need to give them time to perform these task. In my experience, we used to give 3 months time from the date of TECO.
Closing 2011 and 2013 should not have any impact with finance. Do execute and check in case of any errors or balance remaining in the order.
I recommend before starting this batch job, do discuss with your FI team
Hope your doubt is clear 
Regards
Terence