If I hit "Stop" on the render queue, will it just delete everything or will it save the video until the point I stopped?

You may or may not have a partial render after stopping the Render Queue.  It depends on the format used in Output Module template.

If you're rendering an Image Sequence, you should have up to the last frame that was being rendered but maybe only up to the last frame that was written to disk.  

If you're rendering an all I-frame video CODEC (for example, the "High Quality" Output Module template), you should have a partial movie file up to the last frame that was being rendered but maybe only up to the last frame that was written to disk.  Note:  If you're using a much older version of After Effects, this used to not be the case.

For either of these cases, be sure to double-check if After Effects finished the frame that was being rendered when the Render Queue was stopped.  After Effects queues the Composition up with "Will continue from" showing the next frame that would have been rendered.  This may need to be manually adjusted the previous frame before starting the Render Queue.   To quickly check the render, import it and add it as the front most layer of then Composition, scale it to 20% to 25% and go to the Out Point of that Layer's Time Span.  Be sure to set this as a Guide Layer or delete it when rendering the Comp again.

If you're rendering a video CODEC that uses a GOP structure (for example, the "H.264 - Match Render Settings - 15 Mbps" Output Module template ), you will not have a partial file as After Effects won't multiplex a partial movie render.

For this case, you'll need to start the Composition rendering again from the original start frame rather than the "Will continue from" frame.

A quick way to check if your Output Module settings resulted in a partial file or not after stopping the Render Queue is to use the Output To location link for the render item.  After stopping the Render Queue, expand the Output Module and click the location link.  If the corresponding Finder or Explorer window opens, it should show the partial file.  If nothing happens, there's no file to reveal.

It probably depends on the codec, I had the same problem and I stopped the video rendering (Pro Res HQ). It just saved the video until the point I stopped