Is it possible to transfer files over SSH by pasting them into the window?
Certainly there are cases where it works. Famous examples include combining tar+ssh to copy files over the wire, without ever writing the tarball to disk.
The sshd(8) manpage notes that SSH is only 8-bit clean if you specify the no-pty option.
data loss while pasting
Not sure why this occurs. It certainly doesn't occur in the tar+ssh case.