Is it possible to transfer files over SSH by pasting them into the window?

8-bit clean

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.