In any case, backup power generators are built into these large data centers, allowing them to operate without interruption during disturbances (and they produce district heating if they are connected to the district heating network).
As an example, an excerpt from the EIA (YVA) documents for Microsoft’s Vihti data center:
For exceptional situations, preparations are made with backup power generators that use light fuel oil as fuel. Bio-based light fuel oil will be used whenever possible. Approximately 2,400 m^3 of oil will be stored in the area at a time. The total electrical power of the backup power generators to be built in connection with the data centers is approximately 265 MW, and the combined fuel power is approximately 660 MW.
So these are meant for disturbance situations and are there anyway, ready for use all the time. A disturbance situation does not necessarily mean a power outage, but can also mean a situation where there is a threat of a electricity shortage. If the situation lasted for days, additional fuel would of course have to be transported to the site by tanker trucks for as long as the situation lasted.
I want to emphasize again that these backup power generators are not intended for managing electricity prices. But there they are nonetheless.