Yes, you can count any child regardless of age in your household for form 8962 as long as they are a dependent on your tax return. However, he does not qualify as a dependent for the Earned Income Credit since he is not a qualifying child. He is not under 24 and a full-time student.
For stimulus payments the child cannot be a claimed on someone else's 2020 tax return and claim a stimulus payment.
Further, the question he will be asked on his tax return is "Can [he] be claimed on someone else's tax return?" Not "Will he be claimed...?
If he meets the qualifications to be claimed as a dependent, whether or not you actually claim him, he would mark the box appropriately and be disqualified from any stimulus payments.
Here is the criteria for a qualifying relative. It appears he meets all these tests.
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The person can't be a qualifying child or the qualifying child of any other taxpayer.
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The person is (a) related to you or (b) lives with you all year as a member of your household
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The person's gross income for the year is less than $4,300.
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You provide more than half of the person's total support for the year.
If he does not meet the above tests then he can file a 2020 tax return with zero income and indicate that he "Cannot be claimed as a dependent" and would be eligible for the stimulus payments in the form of a Recovery Rebate Credit on the tax return.
Here is a link with more information.
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