Steele is not fighting Shivans at the moment, he is fighting Humans. I would guess that he would adopt a specific strategy in order to combat Shivans as best he could and then adapt his plans to keep the Shivans guessing, although ultimately this would be defeated I'm sure he would probably last a bit longer than most.
Where I say his understanding of shivans and their tactics comes in is his ability to sacrifice (similarly to the Shivan tactics we have seen where they sacrifice to learn about opponents) his forces over the short term in order to gain a long term advantage. In battle with the UEF we have seen him make huge sacrifices - both warships ( the 2nd Battlegroup, the Valerie, the Meridian?, The Carthage's air wing, ect ) and the lives of non combatants (the civilian convoys, Elder Taudiganiin, Lunar domes, Earth orbit station personnel) order to gain an advantage over the enemy. He will have to do this whilst fighting the Shivans as well to have any chance of buying enough time to evacuate systems or seal off nodes.
Although both use radically different methods in how they obtain their victories, they both seem to go by that old Sci-fi cliche The needs of the many outweight the needs of the few
Edit - I am not saying that he understands the shivans entirely - just enough to know that what he does is for the best. He knows that humanity will be lost if they are not prepared for the next encounter and part of that preparation is the need to gain Earth's might to help strengthen the GTVA.
I would argue it seems more likely Steele touched the Shivans minds, and got a glimpse of the magnitude of the threat mankind faces in a way which non-Nagari sensitives don't have. But, I think the problem noted about him is probably still valid: it probably hardened his resolve and gives him an ongoing "victory is justified at almost any conceivable cost".
The real question is whether he "understood" that you can't understand the Shivans tactics or strategies since they're just a mirror. It's be pretty neat to see Steele fighting Shivans, and actually using their adaptability against them: imposing tactical restraints on his forces, to guide the Shivans into one tactical pathway and then attacking them with another.
