That's correct. More precisely, the owner's manual and service manual specify 10W30 at any outside temperature above 32F, 5W30 at any outside temperature below -2F, and either viscosity in between those two temperatures.
Also note that at the time the NSX was introduced, Acura was recommending 5W30 (EDIT - as the PREFERRED viscosity at most temperatures) in all its other cars, and moved to 5W20 for its other cars in the later years of production. Their recommendation of 10W30 (EDIT - as the only viscosity at moderate to warm temperatures) was deliberate and specific to the NSX, so don't listen to anyone's silly ramblings about "an old formula".
There's nothing specific about synthetic oil being required or recommended, other than noting that it's acceptable. But if you want the advantages of synthetic - better resistance to breakdown when hot, better flow characteristics when cold - then by all means get synthetic oil.
Yup. Also note that if you're going to buy full synthetic Pennzoil Platinum in five quart jugs at Walmart for $24.97 before the end of this month, you can get $10 back by mail (limit 2). Click
here for details.