Yes. You need to report this information on your tax return, if you would like to claim an education benefit. The education benefits are based on qualified education expenses that you paid in 2016 and this includes expenses you paid in 2016 for classes that begin in the first 3 months of 2017. 

Additionally, for the American Opportunity Credit, page 10 of Pub 970 says, "for at least one academic period beginning (or treated as beginning) in 2016, the student both: was enrolled in a program that leads to a degree, certificate, or other recognized educational credential; AND carried at least one half the normal full-time workload for his/her course of study. The standard for what is half of the normal full time workload is determined by each eligible educational institution…."

It also says, "For 2016, treat an academic period beginning in the first 3 months of 2017 as if it began in 2016, if qualified education expenses for the student were paid in 2016 for that academic period".

 Per page 11 of Pub 970, "an academic period includes a semester, trimester, quarter, or other period of study (such as a summer school session) as reasonably determined by an educational institution….." https://www.irs.gov/pub/irs-pdf/p970.pdf

 With the respect to the Lifetime Learning Credit, you would need to have taken at least one course during the year. However, you can also claim this credit if your academic period began in the first 3 months of 2017.

Please refer to the following FAQs to learn more about these credits.