Will it?

No. Just do NOT play the file while you have Dawnguard uninstalled.

It will crash if you try and play it with Dawnguard uninstalled, but if you keep the file it will work after re-installing.

I'd back it up on a usb just in case.

It'll be there, but it won't work, like others mentioned.

You can use anything that was saved prior to playing Dawnguard just fine, but if you want to use files that have been saved since playing the DLC, then yes...you need the DLC.