No.
To clarify:
The car doesn't weigh any more than it did before.

Less if you count the missing coil?
Two, you have to understand just how much weight is at each corner of the car and how much compression is on the spring AND how many coils you cut.
Assume you cut ONE Coil; The designer factors in the maximum load (published on the car door sill sticker) and the maximum travel distance for the spring. Then he adds a little margin of error for the moron who overloads the car and hits a dip at high speed so that it doesn't bottom out.
If you cut one coil then you remove a portion of the travel when the car is fully loaded and you may bottom out on a hard dip, but otherwise it should handle exactly the same since the normal spring travel is much shorter than the whole compressible lenght of the spring. Handling would get screwy only when the spring bottomed out.
If you still are unclear, you will have to look at the mathematical expression for the force of a spring = -k*x
which tells you that the spring generates more force as it is compressed a distance x. If you shorten the length then you limit the overall force the spring creates. You can calculate just how much ultimate force you will need in the spring by determining the total load with forces applied while driving and seeing how much travel distance is available in the spring. If you cut more than that then you will bottom out and handling will go to [censored].
This is the bounce people are talking about.