Yes, process IDs may be recycled by the system. They become available for this as soon as the last handle to the process has been closed.
Raymond Chen discussed this matter here: When does a process ID become available for reuse?
The process ID is a value associated with the process object, and as
long as the process object is still around, so too will its process
ID. The process object remains as long as the process is still running
(the process implicitly retains a reference to itself) or as long as
somebody still has a handle to the process object.
If you think about it, this makes sense, because as long as there is
still a handle to the process, somebody can call WaitForSingleObject
to wait for the process to exit, or they can call GetExitCodeProcess
to retrieve the exit code, and that exit code has to be stored
somewhere for later retrieval.
When all handles are closed, then the kernel knows that nobody is
going to ask whether the process is still running or what its exit
code is (because you need a handle to ask those questions). At which
point the process object can be destroyed, which in turn destroys the
process ID.