No, the dependent needs to be a citizen or resident of the US to qualify for the $500 credit.

However, claiming the dependent may still have benefits.  A few of the possibilities are (1) could qualify for Head of Household, (2) medical expenses would be deductible, (3) household size would be increased for the Premium Tax Credit, and (4) there may be State benefits.  There are likely other things as well (I think there is at least one other thing that I am forgetting).