Not necessarily. It only takes about a play or two to recover from getting your wind knocked out. Especially after you add in the time it takes for them to get off the field.
I'll notice even you said "or two" for a specific thing which is really a non-injury. I would add though you can't even communicate with someone who has the wind knocked out of them immediately, so I'm not talking about just recovery.
A: Player has to recover.
B: Player has to be evaluated.
C: Player has to be determined to be ready for play.
I don't think you can generally speaking, obviously there are some exceptions, be expected to do all of that within the time frame of a single play, unless of course the player is faking. Making it three plays for example on a mandatory basis would both discourage faking injuries and make sure actual injuries had time to be evaluated.