The application process involves a background check of both the alien and the petitioner. As far as I know, the burden of moral character is placed on the alien and not the petitioner. Despite that, it may be a problem. Its best to talk to a qualified immigration lawyer.

On a side note, why would someone want to marry a person with such an extensive criminal background? I know love is unconditional but damn.....
I really hope you're not asking for yourself.