Nimzo Indian Classical Line

So there's this one line in the Nimzo that goes like this: 1.d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. Qc2 Bxc3 5. Qxc3 Ne4 followed by ...f5. I cannot find anything on this line, and stockfish only gives white a +.3 evaluation. It seems to allow black to play ...Ne4 without having to reckon with 5. e4 (the number one deterrent from this line). Has anyone looked at this line/personally played it?

which stockfish at which depth?
stockfish17.1 NNUE at depth 34 gives a 0.6 eval after f5.

now this line is ... ok. 0.6 is not outright terrible but this is really more of a testament to how healthy the nimzo indian in general is where even "bad" lines tend to not be much worse than 0.6-0.7 and at least playable. But it is clearly an inferior line. 
In general, black in the nimzo indian needs concrete justification to hand over the bishop pair . Usually this justification is the doubled c-pawns being a permanent weakness and often a correct color square-bishop complex. For example compare this line to this :

its clear, why a line like this is clearly superior. Black can immediately inflict structural damage and can even reclaim the bishop pair lost immediately if he wants to. 

In your line white will simply play in a normal fashion, say nf3 g3 bg2 0-0, and take his sweet time because he has more space and the bishop pair. What exactly does black have in return for this? he has a picturesque knight on e4 sure but what exactly is it doing there besides looking pretty? White can take forever gaining a bit more space or better placing his pieces and release the tension at just the right time. The best thing about blacks position is that his structure is sufficiently healthy and flexible that with very good play he shoudnt be too much worse . But its pretty obvious that compared to the mainstream nimzo indian lines or even the sidelines with clear goals, this line is inferior.

The reason you can't find much is 4...Bxc3 is highly dubious at best. You should be waiting for a3 by White before you take for many reasons.

1) By taking immediately, White maintains the a2-b2 pawn structure, maintaining flexibility. If Black gets a pawn or Knight to c4, White can kick it with b3. By forcing White to advance the a-pawn to force ...Bxc3 or ...Be7, White must spend a tempo, and also weaken the light squares around the queenside. Playing a3 actually weakens c4 too. If White then tries to play b3, then in some cases, a3 may hang. If he plays b4, the c4, b3, and other light squares around there are forever weak.

2) Another factor is the unopposed Dark-Squared Bishop. Without a3 played, White has the simple b3 and either Bb2 or Ba3, preventing castling, hitting the rook, or pinning a pawn to the rook, depending on Black's position.

Instead, against 4.Qc2, there are 3 better options:

A) The flexible 4...O-O

B) The aggressive 4...c5, where 5.dxc5 is often answered by 5...Na6

C) The positional 4...d5 where 5.a3 you take with check and 5.cxd5 Qxd5, the Queen will often go to f5, and after the Queen trade, Black gets dominance on the light squares with a bind.

Don't take on c3 until a3 has been played.

I don't like the Qc2 line. Too passive. But I think I would play e3, Ne2 and then f3. If black moved the c pawn I would play a3 against the Q check.

Qc2 is better at a high level.

I get what everyone's saying, but I'd like to show the biggest reason why I would want to play this line:

There is so much theory in this line and (while the eval bar says black has equality) there's not much to play for. Of course if White plays 5. a3 there isn't really a problem. In that case, the biggest draw for me is the amount of time White loses on the queenside after ...Ne4, and following up with ...f5, ...b6, ...Bg7 and maybe even ...Rf6 at some point seems really strong. Taking on c3 immediately avoids 5. e4 (as I originally stated) and still allows this setup. So my question is: does this still maybe work? (BTW the fact that I may never see the above line doesn't really matter that much to me: I'd rather avoid it then hope it doesn't happen)

If you want something more systematic and relatively "low maintenance" , why not play the zurich variation ? white retains a 0.5-0.6 edge in the most critical lines and similarly, black forfeits the bishop pair without doubling the c-pawn but the lines practically play themselves as far as ideas are concerned.