This is not correct, even if the operating system handles the cache it needs to reheat the pages that are used in order to cache the memory mapped file.
So usually for instance you have a big MongoDB database but the application accesses the database in a very biased way, there is an obvious working set. Part of the working set ends being cached on memory pages by the operating system virtual memory system, so many times when you do a database read operation you read reading from memory.
If the server is rebooted and the MongoDB process restarted the file is not cached in memory, so the first access to every different "page" of the file will actually seek and read from the disk.