Answer
No.
Work Step by Step
The experimental results from the Stern-Gerlach Experiment show that the z component of the spin angular momentum is:
$$S_z = m_s\hbar$$
where $m_s$ is the spin quantum number, and has values of $+\frac{1}{2}$ and $-\frac{1}{2}$.
The only way for the spin angular momentum to be in the x-y plane would be if $S_z =0$ is if $m_s = 0$ which is not the case.
