Under load, the span of chain that runs from the rear cluster to the chainring is tight. Shifting in either direction, the front derailleur knocks the chain off of one ring and drops it onto the other. So when you shift under load, chain tension is suddenly momentarily released, possibly snapping back toward the rear cluster, and then suddenly re-engaged. Possibly, this snapping back could cause a wave in the chain that could conceivably, jump over the cluster.and put some weird tension on the jockey pulley, especially in a small-small combination. But I've never seen it happen because all of my observed shifts happen on the workstand and my left arm can't apply the same kind of force as a 160-lb rider standing on the cranks. Regardless, shifting the front under load can cause damage to chains, chain rings, and front derailleurs, and booggered shifts.

It takes a lot of force to derail and re-engage a tight chain, because it's less flexible than a loose one. It's asking the front derailleur to do a lot work.The rear derailleur has an easier job. The only tightness it's working against is the spring pressure from its tension arm. No matter how hard you're riding, the tension on the lower span of chain is no greater than what that spring can provide. That's pretty light compared to a 160-lb rider standing on the cranks.. I know you don't want to hear this, but your equipment will last longer if you momentarily back off the pedal pressure through your front shifts.
And for chain suck, check the wear on your inside chain ring.