Can't speak for anything less than a Core 2 Duo (P8700 @ 2.53 GHz here) but when I'm doing a decode with DSD+, be it P25/DMR/MOTOTRBO/NXDN/etc, I see the decoder using 5-8% CPU and that's in situations with both slots/channels being decoded for voice content simultaneously; one slot/channel is about 4-5% typically, and this is with SDR# providing the audio signal. If you're just using a true discriminator tap to DSD+ I'd guess it should be about the same without the overhead of the SDR program on top.
I've seen reports from other people that use DSD+ with Atom-powered Netbooks without issues so it may work just fine with those, I just don't own such hardware for testing purposes. I have an older Pentium-M laptop around here someplace but I don't use it much anymore, could break it out and copy over my SDR# folder (where all my SDR-related stuff is located) and do some testing if needed, but I'd hazard to guess it would still be able to handle it just fine.
If you're using such a machine for multiple things at the same time then obviously it won't do as well, but dedicating a Netbook for decoding purposes alone should be workable. Any CPU made in the past 4-5 years should easily be able to handle DSD+ without issues (Intel Atoms and AMD Zecate APUs, low end Intel Celerons and Pentiums, AMD APUs, etc).
The difference between genius and stupidity?
Genius has limits.