Gaussian Process Regression: does feature normalization affect final log-likelihood of model?

Question

I'm trying to learn a Gaussian Process Regressor in SKLearn.

I tried it both with and without feature (and output) normalization, and even though results seem similar-ish, the reported log marginal likelihood differs a lot (-5000 vs 9000)

My intuition would be that the log likelihood would not be very dependent on feature normalization.

So, my question is: does feature scaling have an effect on the reported log-likelihood?