My son did not claim any healthcare on his tax return.
Yes it will.
You household size on your tax return is now smaller, so you qualify for a smaller Premium Tax Credit ("subsidy").
You also need to enter and "allocate" the 1095-A on both your tax return and your son's tax return.
https://ttlc.intuit.com/questions/2954490-do-i-need-1095-a-if-i-m-covered-under-parents-health-insur...