Can we estimate two simultaneous equations using a single-equation technique such as GMM, instead of system estimation technique???

P.S: I have the same independent variables in both equations. These are like this:
Eq 1 Y1 = f(Y2, X1, X2, X3, X4, X5)
Eq 2 Y2 = f(Y1, X1, X2, X3, X4, X5)

Actually, I got this idea from the following post:
https://www.stata.com/statalist/arch.../msg00942.html.