No. You can not. Turbotax Online version works only for current year (2016) tax returns. Turbotax for 2011 is no longer available. Note that the time limit to file a 2011 tax return to get a refund expired in 2015, and the IRS can not issue a refund for that tax year.

If you still want to file for 2011,You can download the Forms and Instructions free from the IRS web site at this link:
http://www.irs.gov/app/picklist/list/priorFormPublication.html