In theory no, in practise it depends.
It really depends on how much data the program is working on, how often the program is run and whether or not it is running constantly.
If I have a quick program that reads a small amount of data makes a calculation and exits, a small memory leak will never be noticed. Because the program is not running for very long and only uses a small amount of memory, the leak will be small and freed when the program exists.
On the other hand if I have a program that processes millions of records and runs for a long time, a small memory leak might bring down the machine given enough time.
As for third party libraries that have leaks, if they cause a problem either fix the library or find a better alternative. If it doesn't cause a problem, does it really matter?