Yes, on average.
Consider twice before significantly polluting the GPP pool. Mere 5-15% chance will pop up all the time, because "unlikely" doesn't cut it. Probability and statistics aren't your friends except in sample sets that could easily devour all the games you ever play with a specific civ and strategy and not show a difference.
I've been experimenting with Altar victory where I pollute the Great Prophet point pool with Great Sage points until I can run enough Priests. Still not sure if getting a single Great Sage that I didn't really need (after capital and maybe 1-2 other suitable cities have Academy) is ever worth it because it might delay the altars much more than the added GPP speed things up early on. (Original plan/hope is that 1-2 Great Sages is ok just because Altars take quite a bit of research in the long run.)
You really have to ask yourself how badly your strategy will suffer if the next great person isn't of the planned type. A lot of waiting for the next one. Generally in non-altar games I aim for a sage or priest first for a specific reason, then later mix the pool a bit while prepared to try and make the best use of whatever pops up. Wonders, Inspiration spell and other things can make it harder to keep the point pool pure, too.
So most of the time, I suggest adding some Great Commander points to the pool but not expecting too much. It could be a nice surprise some time. Just aiming to be the first to research Military Strategy is more viable. The amount of beelining it takes depends on the difficulty.