I don't think so.
As we said in your other "Act of Aggression 2 ideas" topic, it could only advantage a little more unit preservation and micro on the battlefield, specially in early game. The HP buff will still be present, even if the prices are reevaluated.
We can see that the economy of the game is quite comfortable early enough. Currently the game is encouraging the rushes, the basic spams, quick expansion and rapid tech researches. Too early in the game, without progressivity. As a proof, we made several threads about the tier 1 gameplay phase missing for example.
Then, we can make another observation to comfort this idea : The problems with the formations : they're too big, too early, and we end up with blob fights. groups are too big to cross a bridge or find their way in narrow passages, given the pathfinding and formations issues. We end up with blob fights ending in 10 seconds and we have a quite poor control on them. Microing more little groups cause the units will cost more, but with better HP levels, will improve the combat gameplay and the formations' handling. with all units.
In addition to that, higher prices will also advantage the progressivity of the map occupation and reinforcement phases. We would have less local blob fights, ending in 10 seconds and leaving a vast empty map for a minute or two. Also less turtling and mass groups idling on the map in the last third of the games, in SP or MP. Instead of that, little skirmishes will pop out at several places on the map and will last longer. The reinforcement phases will be more progressive. This progressivity will also impact the counters, the snowball effects and the frontline movements.
Finally, higher prices but better HP levels will benefit to the engine and the response time of the units. All of them. The population stays infinite and so the gameplay will still be influenced by brute force economy as you said, like all "good old" RTSs, no problem on that... but the number of units on the field will grow in a more progressive way. The combat will gain some form of persistence and will grow more progressively all other the map, while preserving a better sense of tactical combat. Both at early game and later. The player will also have more critical unit production choices to make, cause the combat will still last while the reinforcements, less numerous, will be produced and driven to the field...
As we said, we could finally find a battlefield pace fitting with the economic pace of the game. That's a strong feeling about AoA, since the first beta. I sincerely hope that those suggestions are evaluated somehow, and that some patches could enhance the game a bit more. It's certainly doable.
That's the saddest part of the story. I was getting used to think, after nearly three decades of its existence, that the word "Strategy" was the main cornerstone of the RTS genre and golden age.