I don't believe it would, no. to a certain extent it will depend on the flow velocity - what sort of flow velocity in the pipe and the insert were you thinking of? Any sort of swirl or uneven flow will switch flow from one side to the other. Maybe o the way in include a flow conditioning plate?
The vertical flow velocity is unlikely to be equal either, due in part to the turbulence created by that sudden change of diameter / change from round to square.
I would make the in and out pipes at least equal to the height of the cut out for as far back as you can go and make the section square rather than round
how even does it need to be?
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