VPN companies get bombarded with DMCA-style copyright infringement notices due to users’ activities all the time. Some prefer to cooperate with copyright holders, to the point of handing over the names of infringing customers for further legal action, while others simply try to keep copyright holders happy by issuing warnings, and ultimately disconnecting repeat offenders.
Some providers, however, are happy to let customers P2P download, and make a good business out of protecting their identities (keeping no logs is always a good start here!) If your VPN provider allows P2P then you can download in safely.
Perhaps more than anyone, however, downloaders should be careful to use a VPN kill switch as they often leave torrents to download unattended for hours at time…