Do US Universities commonly offer admission without funding?
Tough to predict how it will be handled with certainty. You could list the scholarship but then say in your SoP something along these lines: "I've earned in fact (a prestigious?) scholarship from my home government which would allow me to... however it comes with a requirement  that... which frankly I'd prefer not to commit to. Thus I would much rather be admitted with financial support from the university, in which case I would turn down the government scholarship."

For highly ranked research universities, I'd say it is not common for Ph.D. students to be self-funded. That said, if they can grab a strong student who is self-funded, what's not to like? :)