Yes it does..same as now HSE retain enforcement in scarey places like nuclear installations, ships being repaired in dry docks and constructions sites when only the construction workers are there. If other relevan t persons are affected i.e. when a building is going through a refurbishment the fire authority will look after the safety of non-construction workers.
CDM Regs as I understnd them, deal with general H&S, not specificaly fire. Shouldn't cause a problem as both RRO and proposed Regs will require responsible person to carry out a suitable & sufficient risk assessment and record the significant findings.
The only problem may occur if RRO definition of significant findings differs from HSE guidance. That surely could never happen and if it did respected consultants like Mr Todd don't see a problem...and Mr Todd is an honourable man!