Blueprints exist but generally not en route to an emergency
The computer systems shown in these shows is called Computer Aided Dispatch (CAD). CAD is a big deal in emergency services. A well-funded city can have computers in every police car, ambulance, and fire department vehicle. CAD provides up-to-date information to every unit responding to an emergency. Despite all the information available via CAD, I've never seen a computer showing a blueprint. Your question made me curious so I dug into it. Here's the only reference I found to blueprints from a CAD vendor (emphasis mine):
The InterAct system also allows pre-populated choices for location, code, etc. This can be programmed as an auto-fill or a drop-down box. An agency can add any kind of information into the system, including warnings, prior incidents, and resident information such as medical needs or the location of a fire key. A building blueprint could also be added.
So vendors are thinking about the ability to add blueprints to dispatch systems for buildings of special interest.
Thinking more broadly, there are databases of building designs in some cities. Builders have to submit designs for approval, and some cities have started to gather those designs into one centralized place for public review. The vast majority of SWAT missions are planned well in advance, so there's plenty of time to review building plans if they are relevant.