It makes a BIG difference because USCIS would argue that since you two are from the same country - you are familiar with the language/culture/customs of your wife's home country. Not only that, all your family members are also from the same culture. Which means, even if your wife is not allowed to stay in the US with you, there will be no hardship on you since you could just go back to her country to live with her WITHOUT any significant trouble to readjust into that culture. Look up 212 waiver cases and this argument has been used many times successfully, as well as the decisions have been upheld by BIA.
Same for the financial ties - unless you have millions of dollars at stake, you will have no significant trouble to move back with her.
Look, the BASIS of her waiver application would be that if she is not allowed to stay in the US with you, YOU will face EXTREME hardship. But if there is a way to avoid the hardship without significant trouble, there is NO hardship - so no waiver.
Think about this scenario - a US citizen who is married to his wife from India. The US citizen has never been to India - doesn't know jack about Indian culture, doesn't know the language, has no family members there. On top of that, the USC is disabled and 100% dependent on the Indian wife. Now, if the wife is found inadmissible and she files hardship waiver, she might have a case - it would be of SIGNIFICANT TROUBLE for the USC to move to India to be with his wife, also since he is dependent on her, he needs to be with her.
And, yes, your wife could file I-601 while in the US. But she needs to file I-485 first. However, if she is put in removal proceedings and if you are still an LPR at that time - through her marriage to you, she won't have any grounds for "relief from deportation" - so 601 wouldn't even matter.
So, there are only two things you can do -
1. Become a USC ASAP and pray that your wife isn't put in RP before that. Then file AOS for her.
2. Your wife leaves on her own - if she is subject to BAN, she can apply for a waiver and pray that it goes through. If it does, she can come hack to US with an IV.