There are stance emotes, but they are overridden by any power-oriented animation.
The simple answer to your question is no, there's no way to change the default stance of your character in this game. 
Loth 50 Fire/Rad Controller [1392 Badges] [300 non-AE Souvenirs]
Ryver 50 Ele� Blaster [1392 Badges]
Silandra 50 Peacebringer [1138 Badges] [No Redside Badges]
--{=====> Virtue ♀
Is there a way to make it so that your character always stands with a certain stance?