'sheer consequence' is correct and usable in written English.
You could use it to refer to the results of a situation that are particularly severe or intense. For example, "The sheer consequence of the hurricane was devastating, leaving hundreds of people homeless."
Acres of some of the costliest real estate in town have been turned into arcades and squares as a consequence, but sheer space, the urban sociologist Holly Whyte famously observed, is not "of itself" what people need or want.
The slow pace of the shift is, in part, a consequence of sheer volume -- there are more than 140,000 special education students in New York City, a number that is larger than the entire student population of many school systems elsewhere.
Precious information was concealed out of sheer terror of the consequences.
What prompts my wariness about intervention is the cost in money and lives, the uncertainty about consequences, the sheer number of threats we face and the egregious experiences we have had in a variety of cases, such as Syria, Libya, Afghanistan and Iraq.
This offers a basis for the consequences of the sheer number of employees, a routine measurement of organization size.
This is a book of gravity and consequence that is a sheer delight to read.
In "Consequences," crucial encounters occur by sheer chance, by a hair's breadth.
It may be that as a consequence of the multiple sources, and sheer volume, of data about anabolic steroids, in particular on the Internet, users become less critical about the accuracy of this information.
Aside from the sheer number of people living with the physical consequences, LF exacts a crushing economic toll.
What the city objected to was the sheer existence of the playhouses and the social consequences of any form of theatricality accessible to such a broad spectrum of the population.
