In short, no.
It could in theory be possible if you made an intermediate device that implemented a master interface to the hard drive and two device interfaces to the computers, but the complexity of building such a device makes it very, very unreasonable.
It's better to look at other options, like connecting the hard drive to just one PC and then sharing it as a network drive across ethernet to the other PC - or, if you buy a NAS drive, both computers can just connect to the drive via ethernet, no USB involved.