If it was illegal to make the entire copy, it is illegal to copy half the file. See also, e.g., Basic Books v. Kinko's Graphics Corp., 758 F. Supp. 1522 (S.D.N.Y. 1991)
In response to the question of whether moving it to someone else's servers makes a difference: it is the act of copying, not the possession of the copy, that is the violation of copyright law. As for the copy a service assists someone to make, contributory liability would be the issue.
You don't need to be the person making the copies to be contributing to the infringement--material contribution to the copying process and knowledge of infringement run a serious risk of creating contributory liability.
If seriously considering such a service as a business model someone would need to consult a copyright expert with technical knowledge or pay counsel with technical knowledge for a good bit of time to do some research. There are major civil and criminal consequences if the industry or the government decides to go after a service doing this, so legal expenses would be a significant and important cost of doing business that would significantly increase barriers to entry.
In addition, the service would likely be in violation of its agreement with storage vendors, who would want to minimize their legal exposure and might well discontinue the service when they learned what it was doing.