I recently obtained a Sirius II genlock as well, including manual, leads and software (congratulations, it's a nice genlock) :-)
As to the serial connection, according to the manual, this is a regular serial cable. Framiga is also right in stating that the serial port is only needed if you want to control the Sirius II from your Amiga using the included software or using your own scripts (it has ARexx support).
Please note, that the serial lead is also used to draw power from the Amiga. If you do not connect the genlock via the serial port you'll need to power the Sirius II using a 12V adapter. Also if you have a lot of other peripherals connected to your Amiga, supplying the genlock with its own source of power is probably a good idea, whether you have the serial cable connected or not.