Glad you brought this up..
short answer =
YES!
Of course - as with anything else there are a few minimum conditions that must be met first,
the braking system on that 1000 lb car must provide adequate stopping force to still be capable of locking the wheels with the full 1500 lbs of weight at that speed (lets say 60 mph).
Also, the tires can't be bicycle tires - they must aslo be able to handle the 1500 lbs under extreme braking without overheating
as long as these basic minimums are met - then yes - stopping distances would be the same (all things being equal). Some minor variences would of course occur depending where you added that weight - and certainly if that 500 lbs of weight was added as water! (bad).
without going too deep into details... I do have a very simple example that should
help to make sense of it all.
Picture a 1000 lbs car and it stops from 60 in 100 ft (example data of course).
A. now, if you add a 250 lb trailer with a 250 lb payload (500 lbs of additional weight) balanced to have a 0 lb tongue weight - the 1000 lb car now of course unquestionably will take
much longer to stop
B. instead of a free rolling trailer trailer - add 500lbs to the car - but add the weight at or near the already existing center of gravity (perhaps 2/3 large passengers - don't just add 500 lbs on the roof - that would significantly change the COG. Now you have a 1500 lb car - and yes it will stop as quickly or as short as the 1000 lb car. all things being equal.
in example A - significant inertia was added, but nothing was done to increase the traction. - longer stopping distances is the result
in example B - significant inertia was added, but traction was also increased by the same amount - more weight on the wheels.
This very concept is one of the permitting factors behind why an F1 car can decelerate at up to 5g when traveling at full speed. - but can hardly exceed 1.5 Gs of deceleration when going slower (no downforce).
http://en.wikipedia.org/wiki/Formula_One_car
http://en.wikipedia.org/wiki/G-force#Typical_examples_of_g-force