If the LW had just had a third biological child and were asking whether it'd be okay to send that child to public school when their older siblings went to private, I'd say absolutely. Family financial situations change over time (and additional children change the financial situation). But when it's your adopted child that you're treating significantly differently from the other two, and you're planning this before you've even adopted them? No.

Also, if the older kids will be in middle school by time the baby is school aged, why not send the older kids to public middle school or public high school) and send the baby to private elementary? Then the baby gets the benefit of better early education (assuming the private school actually is better; some aren't), and the older kids get a change of environment and peers at a reasonable time to have a transition.