No more or less chance that really anything else connected to power to catch on fire. Just make sure RCD works.

Hell, some weeks ago my oven decided the lower heater's line is now connected to ground and blows fuses...

Our 8 racks in DC only had single event of something blowing (power supply) and aside of smell and fuse blowing nothing really happened

Servers are essentially metal boxes with a bit of glass-reinforced epoxy and some plastic inside so there is limited amount of stuff that can burn. UPS is probably bigger problem

For example the OVH datacenter fire was more of "stuff around servers was flammable" (they had wooden ceilings for some reason...) rather than "just" servers.