Yes, generally speaking, the runway can be used. That said, whether or not it will actually be done depends on many different factors, such as the type of emergency, the size of the airport (maybe there are multiple runways), the current traffic load, the emergency response required etc. The fire marshall would most likely be the only person who could actually decide to close the runway, but ATC could, in practise, decide to not let anyone else land until the emergency is over. It depends.
From an ATC point of view, it may make more sense to get other flights on the ground before the emergency is due to land, instead of having to deal with airborne holdings and possible diversions. However, the risk of another aircraft breaking down and blocking the runway is non-zero, so if the inbound emergency has absolutely no other choice than to land on that specific runway, maybe just closing it for other traffic is the better option.