No, I think that Viola was playing coy. She eventually does find love. Viola is clever because she is a survivor. She dresses as a boy because she is a survivor. By passing messages back and forth, she makes herself instrumental to the plot.
So basically she is not submissive but quite strategical. Can we also say that she disguised herself as a means of survival in Illyria, the land she is not familiar with; or was it a sort of last resort plan, seeing how her first plan was to work for the duchess, who was also mourning for the loss of her brother?