No.
Didn't SW22 post something about rolling discs with illustrations some time ago?
Once rolling it's less a flying disc and more a wheel. Regardless of the disc's stability, how much of the disc's center of mass (COM) is off the plane of the rolling edge will determine which direction the rolling disc turns. Since every disc I can think of has its COM above the plane of its outer edge, they all will all eventually turn towards the top of the disc when rolling and, ultimately, fall over onto their tops because the weight is pulling to that side. The only exception is an extremely angled cut roller. How long a disc can roll without turning is a factor of that COM and how fast it is spinning (gyroscopic stability).
In other words, the stability of a disc used as a roller is only relevant to how it gets to the ground to begin rolling. Once there, the COM in relation to the rolling plane, the angle of the disc in relation to the ground, and the spin rate will determine roll behavior, not stability. I think where confusion creeps in is that there is a correlation between COM being above the plane of the discs edge, which contributes to overstability. But it's not the overstability itself that is affecting the roll.