In theory yes I think. In reality it will be refused because there will be an investigation if it is a real marriage of love or a marriage to get papers.
To get married you need to produce documents and to swear to the truth of what you have written on the marriage certificate, so if you are illegal this would be hard to do for an offical marriage in...
Yes, in fact, many Illegal immigrants will marry US citizens to get attempt to get legalization in the US. Upon marriage, the former Illegals would gain the benefits of a Social Security number, and...