No-
unless you are in the military.
The Earned Income Credit requires US residency. Not taking the exclusion doesn't improve your chances of getting the Earned Income Credit if you weren't in the US for 6 months during 2016.
In some cases, taxpayers can live in the US for more than half the year and also be outside the US for a portion of the year. The foreign exclusion doesn't have to be based on a calendar year- it could be 8/2016 to 7/2017, for instance. In this situation, the IRS makes it known that the exclusion will prevent the EIC. If you are not in the US more than 6 months of the calendar year, you are excluded from EIC consideration from the start.
Its quite difficult to get the EIC if you've lived overseas for any substantial period.
Residency
Child must live with you (or your spouse if you file a joint return) in the United States for more than half of the year
see Rule 14-
