Yes, US citizens can sponsor foreign nationals both within and outside the USA for green cards through marriage. The process itself (current status or no status) to green card easily takes 2 years. Once that person arrives, they can get citizenship (not residency) within 3 years.

The sentence structure though seems to imply marrying solely for status, which is fraud, and reflects very poorly on both applicant and petitioner. This kind of thing definitely happens which is why it takes 2 years for the honest applicants to get though, as the immigration system doesn't do a sufficient job filtering out fraud at the beginning stages of the petition and leaves too much of that work at the end of the petition stage (interview) which is where the biggest bottleneck is.

source: personal experience as petitioner