In my experience there is no real need to remove the RNA from a miniprep prior digestion. However, if you want to visualize and/or purify some of these restriction fragments on an agarose gel, it could be convenient to add a little RNase (e.g. to the loading buffer) before loading the digestion into the well. Just to avoid the big blot of RNA that can mask 100-500bp fragments. No heat treatment needed, though.

Its not necassary to remove RNA. I've had no problem digesting plasmids with RNA.

In principle, when E. coli-derived plasmid DNA is digested with restriction enzymes then of course there should be little interference from any E.coli derived RNA present. But in practice, in my experience, it is usually better to have removed the RNA using RNAse and cleaned the prep up using phenol-chloroform to remove any residual protein present in the prep. There is usually an early step in many miniprep methods that involve addition of RNase. The removal of RNA is often seen as a way to improve the visibility of the DNA bands in subsequent agarose gel elctrophoresis (because the very abundant RNA is dominantly brighter when stained than the less abundant DNA). Perhaps it is this abundance that causes interference in the interactions between restriction enzyme and DNA target.

I have not experienced issues with restriction digests of crude plasmid minipreps by alkaline lysis or boiling. In my classes, we never clean plasmid minipreps before restriction digests.

I never had any difficulties with RNA in many years.