It'll have to be more than half. The Rays are committing $700M in private funding toward their new stadium. The Royals have proposed $1B in private funding toward a new downtown ballpark they want. Jerry's $200M offer, by comparison, is laughably low-ball.
It's obvious that there's no way in hell that he gets $1B in public funding toward a new stadium that'll be used to enrich his estate (by significantly boosting the value of the franchise). If he or a future Sox owner (after he passes) commits to funding the entire cost of the ballpark itself, then yeah the state/city will likely cover the infrastructure costs at the site.
Is there anything in between where a Sox owner commits to, say, $1B in private funding and the state agrees to cover the rest of the stadium cost plus infrastructure? I have no idea what would be acceptable.