Actually publication 972 says, that you need to have the ITIN by the due date of the return, see quote below.
So my understanding would be, that if you apply on time for the ITIN (together with the return or before as it seems it happened in this case), you would be eligible for the child tax credit for that year (but not for years before that).
<a rel="nofollow" target="_blank" href="
https://www.irs.gov/publications/p972/ar02.html">https://www.irs.gov/publications/p972/ar02.html</a>
"Taxpayer identification number needed by due date of return. If you didn't have a social security number (an SSN) or ITIN by the due date of your 2015 return (including extensions), you can't claim the child tax credit or the additional child tax credit on either your original or an amended 2015 return, even if you later get an SSN (or ITIN). Also, neither credit is allowed on either your original or an amended 2015 return with respect to a child who didn't have an SSN, ATIN, or ITIN by the due date of your return (including extensions), even if that child later gets one of those numbers."
