H1 extension without stamping in US

My situation is:

H1 approved till Dec 31, 2013 but not stamped.


Currently in US on H4.


Employer will change status from H4 to H1. 


Question is: Can H1 be extended without being stamped or more precisely, can H1 be extended even if the employer does not change the status from H4 to H1 before Dec 31, 2013 but agrees on extending it?

So in this case, employer files H-1 extension w/o COS. Yes, they can do that.

What purpose does it solve? From employer’s perspective, it will mean spending more dollars on you w/o surety that you will join them. If I am the employer, I will not be inclined to do this.