Not quite, operating systems tend to maintain a "write buffer" of things that need to be written, I'll try an example:

When you stream a video from the internet, everything tries its best to maintain a few seconds ahead of your current position, so in the event your network slows down, the experience appears to be uninterrupted. The same thing applies to flash drives.

A small write buffer is maintained so that in the event it can't immediately write (for example, a non-asynchronous read occurs, or the USB stack slows), it can take care of that as well as and perform deferred writing to the device. By this point, the file handle from the OS perspective has been closed and the OS has no knowledge of the file being open any more as the buffer is maintained as a list of "write these bytes to this position" at the kernel / driver level.

Now, the probability of this buffer ever having any data in it is pretty slim (in fact, I believe windows will sometimes flat out disable it), as computers are at a point where device speed isn't really an issue, however, if you remove the device PRIOR to this buffer being fully flushed to the device, it MAY cause corruption or data problems depending on what was left in the buffer at the time.

The "eject" mechanism inside the OS is a way for it to ensure the buffers are empty and the device has been finalised before you remove it, ensuring that the removal is 100% safe.