Hmm.. I spy with my little eye a trap with the letter I..
Or maybe I just created that trap myself, but of course what else to expect from my ponder-puddle?

So, I will say:
No, Androgynes are generally
not multi-dimensional thinkers.
And now it's time for my funky explanation on that one.
The way I see it, Androgynes might think they are multi-dimensional thinkers but a lack of wires (binary/gender wise) makes those thoughts pure speculation. The lack of understanding of others frame of reference is calculated and processed (by logics) in an individual frame of reference. So while that frame might have a bit more hatches it's still created from our own speculative observations...
So multi-dimensional? No... Alter-dimensional, likely. We might see more but we have trouble seeing what others see.
Does that explanation make any sense? I don't know. I just thought it fun to take a stab at this.

Edit: bit more of an explanation as to way I decline multi-dimensional... As far as I get there has to be an understanding of the basic dimension and its ruleset in order to be able to apply it to thinking and as explained above I believe ag's lack that understanding.