I guess its time to quite lurking and post a response.
The National Register cannot prevent a building from being demolished. The National Register designation only has “teeth” when federal funds are being used for a project. If federal funds were involved, demolition would be considered an adverse affect and the demolition would either not be permitted, or the adverse affect would have to be mitigated.
I strongly suspect that the demolition would not be allowed if federal funds were used.
The more important designation would be a local landmark designation, which is the designation that actually has some real "teeth." Typically if a property is designated as a local landmark by a city, all city issued permits for the property must be reviewed and approved by the city's preservation commission. I find it hard to believe that any preservation commission would approved the demolition of such an important building.
It is a safe bet that Historic Denver, the non-profit historic preservation advocacy group in Denver, will be actively opposing any demolition.