Every Arab government is “based” on Shariah.
But
#1, Shariah is not a sufficient set of laws to govern a state,
and
#2 without a democratic process it is meaningless because you have no mechanism for removing a corrupt ruler even if the system is “based” on Shariah
…oh, and #3 the ONLY way you will get any semblance of an Islamic society is if the majority WANT it to be that way, because MOST of what makes a society Islamic or otherwise has little to do with the character of the government, and almost everything to do with the character of the population