Sway bar with large diameter t-bars?

Yes, it will. T bars have the job of "Up and Down" movement. There side to side sway or tilting control of the car is limited.

The anti roll bar or sway bars control that aspect of the car. It's there job. And there's trouble if someone else tries to do there job (reliably) in part or full.

Parts on a car are like a union shop. Every one has a job and that's there only job.