Mid/Side encoding/decoding in frequency domain instead of time domain
Yes, it is possible. The discrete Fourier transform (DFT, of which the FFT is an efficient implementation) is a linear transformation, i.e.,

$$
a\cdot\text{DFT}\{x\}+b\cdot\text{DFT}\{y\}=\text{DFT}\{a\cdot x+b\cdot y\}.
$$

The same holds for the inverse transform.

As a consequence, you can directly convert the equations for the mid and side signals from the time domain to the frequency domain. Simply replace the subscript $t$ with $f$:

$$
M_f = \frac{L_f + R_f}{2}\\
S_f = \frac{L_f - R_f}{2}\\
\vdots
$$

From $M_f$, $S_f$ you can then compute the inverse discrete Fourier transform to obtain $M_t$, $S_t$.