Yes, it is possible for built-in functions to not implement the [[Construct]] property. The ES5 spec clearly states the following in the section on Standard Built-in ECMAScript Objects:
None of the built-in functions described in this clause that are not constructors shall implement the [[Construct]] internal method unless otherwise specified in the description of a particular function. None of the built-in functions described in this clause shall have a prototype property unless otherwise specified in the description of a particular function.
At first glance it doesn't appear that any of the functions subsequently listed actually state otherwise.
As demonstrated by Quentin it appears that a number of host objects implement functions without [[Construct]] properties too. If you want to achieve the same you'll have to settle for the solution provided by Ingo Bürk since there is no way to control whether or not the internal [[Construct]] property is set on any function object. The section of the spec that deals with Creating Function Objects includes the following step which is not optional and contains no conditions:
7. Set the [[Construct]] internal property of F...
foofunction then? Unlessfoois an object.