No, the equation I posted relates the electric field at a location P to the "retarded" location of the charge producing it, i.e., the position of the charge at the earlier time when it crossed the past light cone of P. You recover the equation in your OP by rewriting it in terms of where the charge is now assuming it continued to follow a rectilinear trajectory since that earlier time, not by removing some "contribution due to acceleration" term. You're still assuming, for no reason, that the difference made by acceleration is only due to the amount of time spent accelerating. If a charge is not accelerating 99% of the time that does not mean the equation in your OP applies 99% of the time. It doesn't work that way. The charges could be changing direction instantaneously and accelerating 0% of the time as far as I'm concerned. It would still matter and it would still need to be accounted for.