Ha. Never got the tour. We tried but they don’t do the tours any more for anyone. 9/11.

Nuclear plants do use steam from the reactor to cool the core in a loss of electrical power. In a BWR (the type Monticello is), this is typically in the form of HPCI (High Pressure Coolant Injection) and RCIC (Reactor Core Isolation Cooling). Essentially, as long as reactor pressure stays above ~150 psi, turbines that run on steam (or even high pressure water, these are sturdy turbines) can keep the core cooled. The water can be pumped just fine without electricity. However, the amount of steam going into the turbine needs to be regulated to ensure that the turbine doesn’t start spinning too fast and burn out the pump. The valve regulating the steam requires a small amount of electricity to monitor the turbine speed and adjust the valve position. Typically, when the nuclear plant loses outside power, the diesel generators kick in. If that doesn’t happen, there are battery backups. If the situation goes longer than the batteries last, at least some plants have backup manual methods of keeping the turbine running at the right speed.

A high level discussion of reactor safety systems HPCI
A more biased link that explains further the capabilities of HPCI and RCIC (about halfway down the article). Emergency Core Coolant Systems

“Elk River Station is an energy-from-waste plant operating in Elk River, Minnesota that generates 35 to 42 megawatts of electrical power.
The site was originally built as a coal and oil-fired facility in 1950, then was converted to a nuclear power plant (boiling water reactor) in 1963. The nuclear reactor was small and only operated from 1964 until 1968 before undergoing decommission and dismantlement in the following years, ending in the early 1970s.
It resumed operating on coal and oil in 1968.
In 1989, the facility was again converted, this time to use Refuse Derived Fuel or (RDF) for fuel. The RDF is made from municipal solid waste. Waste arrives from Anoka, Benton, Hennepin, Sherburne, and Stearns counties, and the ash remaining after incineration is taken to a landfill in Becker, Minnesota.
Elk River Station is operated by the Great River Energy cooperative.”

Yup!

Even if Fukushima Daiichi had such a system (I have no idea whether this was the case), it would have had to be properly designed and constructed to withstand a magnitude 9.0 earthquake (which we know was not true of other systems at the plant) followed by a 10-14 m tsunami (ditto) and remain operational (unlike the reactors, which should have shut down). The way things unfolded, I don’t think it would have helped, and if the plant had been properly designed and built to withstand an earthquake and tsunami of this magnitude, the diesel generators they did have on hand would have done the job.

There may well be other situations where it would be useful, e.g., typhoon strikes, which while not a major concern in the Tohoku region are an issue elsewhere in Japan.