No, I think she provides a perfect mirror/foil for Toph.
"My parents gave me everything that I ever asked for. But they never gave me the one thing that I really wanted. Their love. " -Toph
"I was a rich only child who got anything I wanted. As long as I behaved... and sat still…and didn't speak unless spoken to." -Mai
The difference is, Toph (and Ty Lee, if you think about it) asserted themselves, established their identities and personalities and desires, and ran away. Mai had to have romantic involvement to be prodded into action: she couldn't come to any decisions on her own. And even then, she did what she did not because she thought it was "right," but because she had a crush.
"My parents gave me everything that I ever asked for. But they never gave me the one thing that I really wanted. Their love. " -Toph
"I was a rich only child who got anything I wanted. As long as I behaved... and sat still…and didn't speak unless spoken to." -Mai
The difference is, Toph (and Ty Lee, if you think about it) asserted themselves, established their identities and personalities and desires, and ran away. Mai had to have romantic involvement to be prodded into action: she couldn't come to any decisions on her own. And even then, she did what she did not because she thought it was "right," but because she had a crush.