Never mind... I had a great explanation of depth of field, and shutter speed, etc, but after re-reading a post that read like a first graders homework, I decided to delete it. Sorry. The long and short is that when you have the lowest f stop you can use to hand hold the camera AND freeze the action, you will very unlikely have so small of a depth of field to get anything other than most of the parade float in focus.
The only offset to this, and it is somewhat limiting, is that you could use a high ISO. This will give you a few more stops of shutter speed, which will allow you to change the apature. Even a tripod will not help, because while you would gain the ability to get the depth of field you want, anything in motion will blur due to the parade moving.
There is 1 other option... you could set up a tripod and take photos of the parade, using a decent shutter speed. Then without moving the tripod or the camera (this is critical) you could take the background photo with a longer exposure (after the parade is over). Then combine the 2 images in post production.