My Question to confirm is -- does WinSCP support file locking when downloading/getting? and likewise, when uploading?
No, because it has to be supported by the SFTP server in the first place. And absolute majority of SFTP servers (OpenSSH for instance) does not support it.
As an alternative you can force transfer to temporary file name, if the BizTalk's File Adapter can be configured to ignore certain files/extensions.