Strictly speaking, yes.
That is not to say the airframe is dangerously unstable in yaw or prone to spinning, only that the tail boom does contribute slightly to tail volume, so, disregarding any weight and balance effects form the fairing and assuming everything else stays the same, the "naked" version will have less lateral stability.
The vertical tail volume coefficient can be defined as:
$$
V_v=\frac{S_v l_v}{Sb}
$$
In the numerator, $S_v$ is the area of the vertical tail and $l_v$ is its moment arm. The denominator contains the wing area ($S$) and span ($b$). Non-tail surfaces are often obviated for simplicity, but a more rigorous expression would be:
$$V_v=\frac{\sum_{i=1}^n S_{v_{i}} l_{v_{i}}}{Sb}$$
where each surface aft of the CG is weighted by its moment arm and added to the coefficient. This would include the boom area.
This coefficient represents the capability of the tail to counteract yaw; a lower value will lead an aircraft that is more prone to yaw, and easier to spin (again, all else being equal).
Susceptibility to spins does depend on CG location, because an aft CG will place the center of rotation closer to the tail, reducing the arm it has to counteract yaw, which translates to less tail volume. In the case of such GA aircraft, the addition of a couple kilograms at most of cloth to the boom structure should not shift the CG out of envelope unless the design is already at its limit.
