No .. The GVWR (Gross Vehicle Weight Rating) is the manufacturer's maximum trailer weight rating when loaded.  

Various state law enforcement people will use it to to give you a ticket for having more trailer than you're allowed by your driver's license .  Even if the trailer is empty, the laws are based on the GVWR.

You will have a GVWR for each vehicle, Truck & Trailer

You will have a GCVW (Gross Combined Vehicle Weight) for the Combination of the two. (Truck & Trailer)

Manufacture specification detail a number for both ratings. When police check your rig they look at both.

Your truck may be under it's GVWR but over on it's GCVW. Or you may be under on the GCVW but over your GVWR

Examples of this are:

Say you truck is rated at 10,000 GVWR,  Empty it weighs 7000lbs.  Meaning you can put 3000lbs of cargo in the truck and still be within it's rating.

Your truck may have a 23,500 GCVW Meaning that the combination of the truck and trailer can not exceed 23,500

If you trailer weighs 16,000 Truck weighs 7,000 your total = 23,000 or 500 lbs Less than your max GCVW

But lets say your trailer has a 3500 pin weight.  This puts the weight on your truck axles (or it's GVWR) at 10,500 which is over it's rating. So you would be legal for your GCVW but illegal for your GVWR.

You will need to be aware of both numbers when you pull through a scale.