How important is the driver tube in a tubed amp?

Does changing the driver tube affect the sound of the amplifier dramatically? I have a 300b SET amp the uses 12au7 tubes as the driver. Would changing these from the stock tubes to a better quality tube make a difference?
Yes, the driver tube can make a significant difference.
Agree wholly with Ncarv, from my experience with Jadis and Lamm amplifiers. As to whether the difference is an improvement, that's another, far more subjective, question that only your ears can answer.
Anything else?
The driver tubes are feeding the output tubes. Whatever the driver tubes give to the output tubes, then that is what you'll get out to the speaker. If the driver tubes aren't getting it, then the output tubes won't either. I'd say that is fairly important. Also, in some cases, the driver tubes are providing alot of the gain in the amp. Also pretty important. Get good driver tubes.
FWIW, for those of you on a budget, rolling driver tubes is not only the cheapest way to experiment with an amp's sound, it can produce the most noticible difference.
BTWI (Before Transistors Were Invented) we ran output tube until they glowed brightly and pulsated with the music. However, input (gain) stage tubes, and to a lesser extent the driver/inverter tubes we replaced from time to time to maintain sonic quality. Thus I conclude that these tubes have greater effect on performance than do output tubes. Besides, they are relatively cheap.
The amplifier circuit/transformers combination and construction style would make 80% of the sound. Parts would contribute another 20% or so. Active parts like tubes would matter more than a resistor. However, in a single ended 300B circuit design, anything matters. Even different resistor or wires would change the sound when using with a high end system. Voicing the amplifier would takes more time and cost more than solder the amp togather.

Tube rolling is cheaper to modify/upgrade the sound performance, but only to a small margin. The foundamental charactor of the circuit is still there.