Yes, the text of the show is explicit that Hansel is a feminine gay boy who is coerced into having a sex change in order to flee East Germany, not to affirm his gender, and then presents as a woman (Hedwig) out of necessity.
The scenario (and the show itself) is certainly very queer, but not clearly defined on any sort of binary, whether it is male/female or cis/trans, which is the whole point. I think forcing it into that sort of box is detrimental.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."