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No, in general for power law RGE behavior which is captured by the Wilsonian approach, but can be missed if we formulate our Continuum EFT using

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body \overline{MS}

and dimensional regularization (Dim.Reg.). But the answer is yes for the dominant logarithmic behavior. If we know what theory we are considering then it is often sufficient to treat only the logarithmic corrections, but power law corrections can be relevant for flows where a theory moves from one power counting regime into another. With a soft regulator like Dim.Reg. we can also formulate a renormalization group for power law terms, by noting that power divergences still show up as poles in other dimensions. An example we will talk about later on is the power divergence subtraction scheme. We will use this scheme to show an explicit example of a flow between regimes with two different power countings.