Yes, that is correct. Technically you both do not fall into the requirement of Form 8332 as you both are not separated or divorced. Filing the form mainly to show the other parent is waiving the right to claim and let you claim instead.
As you mentioned, MFS does not require your spouse to have an ITIN. You might not able to e-file but still can prepare forms in TurboTax. As far as stimulus, only those who have a valid social security number qualify for the payment. ITIN would not qualify.
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