I don't see how, considering the new characters would be introduced with the new content and it would require you to be at a certain level to complete.
In the other games each class also share the same story. Yes, SWTOR is the exception but we are discussing SWTOR. It has set a level of expectation.
Nothing else matters to companions when romancing the PC so I don't see why gender should be different (species, appearance, even morality can be overcome with gifts). Plus, it could still matter (i.e., result in different dialogs) without limiting romance choice based only on gender.
Regardless, the point is that there will be unhappy people if options are limited. Just from reading this thread over the past half of a year, the posters who desire SGRA content have specific companions in mind for their toons and will not necessarily be happy with any old SGRA option.
It's like, "Yeah, I know your female Smuggler wanted Risha, but too bad...you get Akaavi and you should be happy you got something."
Most characters are not all too deeply involved in the class story anyway, apart from the way you pick them up. The existing characters were never designed with the intent to use them for more than one class, and yet I don't see a reason why Tharan for example would work for all republic classes. That the class story is different for all classes is therefore irrelevant, even though it will cause design overhead for integrating them, but that's inevitable either way. If you create different characters for every single class, that will cause considerably more overhead and consequently yield less characters becoming available.
When it comes to sexuality the gender matters a lot. Some people are simple not gay. Of course in some cases we'd like them to be, but the game would be shale if all companions would simply be whatever we want them to be. DA2 is not a particularly good Bioware game - I don't find it bad either, but it's certainly not par with Dragon Age: Origins are the Mass Effect series.