When you "Plan" something during a flashback, there is no character inhabitation going on. It's purely the player coming up with a way to get by the current problem via the flashback mechanic.
Long before Blades and other games introduced flashbacks as a mechanic, we used flashback scenes regularly in my old AD&D campaign in the 1980s and early '90s. My recollection was that even back then people were still inhabiting their characters just as much as they were in the fictional present.
Granted, these flashbacks were intended primarily as a way to add depth to a given character. So they weren't used to add capabilities to the party in the present. But I don't see any reason in theory that this couldn't be done in a satisfying way at the table. I'm intrigued to try it out.
It's more than that. You are also overcoming a current obstacle that you might not have known about or even thought might be present. That alone makes it very different from planning in advance.
Yes, it is different, but I'm not sure that the difference means that you can't remain immersed in your character.
Here's an example of a possibly similar mechanic from my current GURPS Dungeon Fantasy campaign. One of the PCs in a Viking setting was a devotee of the fates. He invested many of his character points on various advantages that allowed him to be far luckier than average. One of these was called "Serendipity" and it allowed him to effectively call for "one fortuitous-but-plausible coincidence per game session."
At first, I was worried that it would be too "meta" and would break suspension of disbelief. The player, too, worried that it would take him out of his character. But we went with it to see how it played. Turned out to be awesome. In order to make the coincidences plausible, the player had to spend a lot of time thinking about his role-playing connections and backstory. Often, the serendipitous occurrences involved him bumping into people that he knew before, giving him better odds on a reaction check. This added a lot of role-playing scenes to the game. The other players loved it. I enjoyed having to be nimble enough to roll with it. The player ended up knowing his character far better than most of the other players. It was a win-win-win.
Obviously, there is a meta-dimension to this. The player had to think about what he could plausibly introduce that would change the odds of a situation in his favor. But, as he described it, it didn't feel any different to him than considering which spell he might cast or what combat maneuver to choose. There was, of course, a cost in terms of resources spent (he could only use it once per session). Sometimes he wasted it on a situation that wasn't as dire as he thought.
Sometimes there were additional costs down the road. For example, he serendipitously ran into his older brothers in one scene. They gave him an edge in a scene featuring negotiations with a minor lord. (His older brothers had more social clout than he did.) Later these brothers were slain—to all of our surprise—in a battle that went very badly for the group. This became a central element of the unfolding story and had a profound effect on the PC.