Can I use IRLS (e.g., Lp-norm) regularization on the gravity and magnetic models while still using cross-gradient as a coupling term?

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I’m working on a joint inversion of gravity and magnetic data in SimPEG, and I want to incorporate cross-gradient coupling between the two models.

I know that SimPEG supports IRLS for sparsity-promoting regularization via Update_IRLS,Can I use IRLS (e.g., Lp-norm) regularization on the gravity and magnetic models while still using cross-gradient as a coupling term? Additionally, both ‘Update_IRLS’ and ‘PairedBetaSchedule’ contain parameters named ‘cooling_factor’ and ‘cooling_rate’.
Do these overlap or conflict in any way when used together in a joint inversion?