It depends what type of head. The JD choppping head , (stalkmaster) is the same design as the italian cressoni and drago as well as the hungarian harvestec. These all rely on the old lawn mower blade technology which Geringhoff abandoned in the early 80's. Of the many disadvantages, the lawn mower blade design results in an average increased horsepower draw of 30%. The Geringhoff (www.geringhoff.com) uses a completely different design which only demands an additional 2 hp per row. Geringhoff only suggests a direct drive when using heads which are 12 rows plus. If using a Geringhoff, your 9560 should have plenty of power even with the variable speed drive which is supplied as standard equipment on the 9560. If you buy a lawn mower blade chopping head, (unlike the Geringhoff) you'll need to buy a direct drive.
If you have the HD reverser setup you might be ok,but in most cases your going to need the fixed drive if you dont want to be blowing belts all day long. Oh and that goes for the gerringoff as well,if its a chopping head, it takes power to chop stalks reguardless of design.
Maybe your condition are different in SE SD I have had a couple customers in the past who had a 9650W and a 9560 with 8 row 30 gerringoffs and we could not keep belts on them even with backshaft speed all the way up. If it were my machine I would put the High Torque conversion drive to keep it a variable speed.