Ordinarily, no. But if you get it going fast enough before it leaves the rod, there's a lot of base drag which brings the CP some way behind the disc and makes it stable, which is why saucers can make stable flights. Once the motor burns out the disc loses velocity very soon due to that drag, making it unstable, so it tumbles down.
Originally Posted by awseiger
A spool without the top disc is basically a saucer with a tube sticking out of the front; the CP will be as far back as for the basic saucer but the CG may be further forward, if that tube contains something nice and heavy such as the front half of a motor casing. I'd guess that a spool without the bottom disc will be in trouble...
I have no idea of the maths behind all this so I can't say how fast a disc needs to go to be stable, let alone how far two discs (i.e. a spool) can be apart and still be stable. But since a spool rocket is (a) never going to move very fast and (b) doesn't have a hard pointy bit, it's relatively safe to mess about with. So some experiments involving a spool with a telescoping shaft or a series of spools with varying shaft lengths but otherwise identical might be in order.
Don't just stand there, get one up!