No, this does not create a new instance of Person and then call a method on it. It creates an instance of whatever Person.doSomething() is. So, in effect, you these two are equivalent:
const Person = {
  doSomething: function(foo, bar){
    this.foo = foo;
    this.bar = bar;
  }
}
//create a new instance of `Person.doSomething`
const p1 = new Person.doSomething(1, "one");
//take a reference of `Person.doSomething`
const temp = Person.doSomething;
//create an instance of it
const p2 = new temp(2, "two");
console.log("p1:", p1);
console.log("p1 instanceof Person.doSomething:", p1 instanceof Person.doSomething);
console.log("p2:", p2);
console.log("p2 instanceof Person.doSomething:", p2 instanceof Person.doSomething);
 
 
You can only get instances using constructable functions. These are plain functions (declared with the function keyword)  and class constructors:
function PlainConstructable(a, b) {
  this.foo = a;
  this.bar = b;
}
const plainInstance = new PlainConstructable("plain", "instance");
class ClassConstructable {
  constructor(a, b) {
    this.foo = a;
    this.bar = b;
  }
}
const classInstance = new ClassConstructable("class", "instance");
console.log(`plainInstance:
  instanceof PlainConstructable: ${plainInstance instanceof PlainConstructable}
  what it holds: ${JSON.stringify(plainInstance)}`);
  
console.log(`classInstance:
  instanceof ClassConstructable: ${classInstance instanceof ClassConstructable}
  what it holds: ${JSON.stringify(classInstance)}`);
 
 
Non-constructable are:
const arrowFunction = () => {};
const plainObject = {
  shorthandMethod() {}
}
try {
  new arrowFunction();
  console.log("Constructing arrow function successful.");
} catch(e) {
  console.log(
    `Cannot construct arrow function
     ${e}`
   )
}
try {
  new plainObject.shorthandMethod();
  console.log("Constructing shorthand method successful.");
} catch(e) {
  console.log(
    `Cannot construct shorthand method
     ${e}`
   )
}
try {
  new parseInt();
  console.log("Constructing built-in successful.");
} catch(e) {
  console.log(
    `Cannot construct built-in
     ${e}`
   )
}
 
 
For more information about constructable functions