The answer is yes, with a big qualification. Taking the log of a value and analyzing it via GLM is NOT the same as using a log link in GENMOD. The first is really assuming a lognormal distribution, while the latter assumes a distribution from the exponential family where the variance is some function of the expected value. A good way to see this is to run these 3 on the same data: GLM on log transformed data, GENMOD specifying a log-normal distribution and GENMOD with a log link. The results may surprise you (they may not if I am saying something obvious to you).
So effect size measures like eta squared and omega squared obtained from GLM on the log transfomed data assume homogeneous variances in the log transformed space. Thus ranking variables by effect size would tell you the relative importance of a variable that is predictive of what is essentially log(Y) + error(Normal, 0, sigma**2). But if your variances are not homogeneous in the log transformed space (like Poisson, negative binomial, or gamma distributed variables), the family of effect sizes from GLM will likely rank variables differently. To get around this you might try the approach given at this link on StatExchange. I interpret this as: hold all of the variables at fixed values (with their solution as previously found) except one. That one you should score the model with two values and get the difference in the predicted value. Repeat as needed until all of the variables have an estimate. I believe this is what the R package emmeans uses for nlme results, but I could easily be wrong.
SteveDenham
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