Yes, this is true. Basically "есть" emphasizes the fact of posession and "no-есть" -- the object of posession.

There are some funny cases when different things have different meanings.

Two people are out on a date, but all of a sudden it starts raining.
She says "I gotta go home, let's catch a taxi". Then he says: (attention)

У меня машина. (It's like I have a car here, I can give you a lift. The car stressed).
У меня есть машина. She's like "oh great, where is it?" -- it's in my garage.

(the latter sounds totally retarded in this context as you have already guessed)