I have an Alinco DX70 and I do PSK31 regularly. You do not need to have VOX. In fact, some would say that it is better not to use VOX for transmitter keying.
I bought this kit for making an interface between the computer and radio
Unified Microsystems: SCI-6 PC Sound Card Interface Kit, and more for ham radio operators!
Works just fine on the Alinco. Unlike some newer designs of radios, you cannot control the radio
(change frequencies, settings, etc.) through the software
on the computer. But that's no big deal. Just set the radio manually and away you go.