Not on a theoretical level, but how would you practically have to pay costs, access specialist doctors?
That is not correct anymore - they are absolutely insured as long as they are entitled to Bürgergeld,even if they don’t actually get it or have the three month block in it. The problem is more that the insurance works retroactively in that situation and they often are billed privately by health care providers (which is somewhat illegal) and some of these claims “stick”, especially if you don’t have the resources to fight it.