Short answer: No.
Long answer: No. C++ will never persist memory unless you do the work to make it do so. The reason to free memory is this:
If you don't free memory, but keep allocating it, you will run out at some point. Once you run out, almost anything can happen. On Linux, maybe the OOM killer is activated and your process is killed. Maybe the OS pages you completely to disk. Maybe you give a Windows box a blue screen if you use enough memory. It can almost be thought of as undefined behavior. Also, if you leak memory, it's just siting there, unused, unreleased, and no one can use it until your process terminates.
There's another reason too. When you release memory to the allocator, the allocator might keep it around, but just mark it as usable. That means that next time you need memory, it's already sitting there waiting for you. That means there are less calls into the kernel to ask for memory, increasing performance, as context switches are very inefficient.
EDIT: The C and C++ standards don't even give a guarantee that the memory will be cleaned up by the OS after termination. Many OSes and compilers may, but there is no guarantee. Despite this, all major desktop and mobile operation systems (with the exception of probably DOS and some very old embedded systems) do clean up a processes memory after it.