Coming from a very different background here - I am a keen archer.
It is normal practice (as with aircraft) to have fins (fletches) on the back of the arrow to keep it straight, but it is also a normal part of "tuning" to remove those fletches from an arrow or two, and shoot them 'bareshaft'.
The point of this test is that they are less forgiving, but because all arrows have a heavy point, the centre of mass is forward of the geometric centre, which means that the whole of the shaft acts as a stabiliser, and given good conditions, the arrow will still fly straight (and this IS largely aerodynamic flight, quite different from the ballistic flight of a bullet).
Going back to what I was saying earlier, it would be difficult to predict how much disturbance it could survive, but a simple, long straight fuselage, with no stabilising fins at all, IS going to fly fairly straight unless/until tubulance goes above a critical threshold. To be fair, this is also true of a glider with 'normal' fins, its just that the critical amount of turbulance is much higher.
One question that doesn't seem to have been mentioned is 'what is the penalty for failure?' - In a manned vehicle, failing to fly straight is considered 'a bad thing' but if your model is allowed multiple flights, then a few failures may be worthwhile if the trade-off is reduced drag.