Paul it still needs brushing in though! Depending on carpet type, even a very heavy application just sprayed on and left won't penetrate and get to all the soiling properly.
Agitation is part of the cleaning process. Sometimes all you need is a quick whizz over by hand with a groomer, other times it's full on with rotary or CRB to break the soiling away from the fibres. Dependfs what the specific situation requires, there's no one size fits all answer.
Jim is it REALLY that much of a bind to carry a Duo up a few flights of stairs? If you think about it you're going to be walking up/down a few times with all your other stuff, it doesn't take much organising so you can carry one more piece of essential kit up with you.
At the very least I'd take a groomer up to the job - you can carry it in the same hand as your wand no problem, just grip them both together. I'd use a colloidal product (m-power or nemesis) as a pre-spray, which as Paul says don't necessarily require as much agitation as something like a microsplitter. I'd stop short of saying they are "self-agitating", sounds a bit silly to me, it gives the impression there's a magic arm reaches out of the product and scrubs itself with a brush!
All you need to do with them is break the surface tension by quickly brushing in by hand after spraying, and let the product do the rest. As Robert suggests, a heavy application will help to speed things up, and leaving it longer will help compensate for less mechanical agitation.
Of course you have the other option which is to forget HWE and just lug a rotary up instead of extraction machine.