technically he should be able too. I won't get into high adamantium is scientifically impossible.. However, for all intensive purposes Marvel says it is unbreakable. So until someone is able to break it. I guess it will stay unbreakable. So my answer is no.
Unless, in Ultimate Hulk vs. Wolverine when wolverine is torn in half his bones are broken. If this is the case than Supes could easily break adamantium