Padding would be necessary unless you decide on a glue down application. It would be like driving your car without shock absorbers.

I heard about a sign above the door in a Southern California carpet store that reads, "Only a rich man can afford cheap carpet." The truth is, with flooring you should always go with the absolute best your wallet will allow. Whether you're talking about carpet, or the cushion under it, heed this advice. I have done warranty replacements where the pad had been down for less than a year and the manufacturer refused to pay for its replacement, but as a rule, always replace the pad when replacing carpet.

Thanks everyone for the advice.  I've decided not to skimp on the padding.