sorry but from experience here, the only thing that really matters when it comes to online gaming is the quality and stability of your internet connection
If you are at the recommended specs for the game, sure. When you are at the minimum requirements, or slightly below, it's another story. There is at least one regular poster in the forums that play solo online because the game becomes a slideshow for him if he attempts open, for example.
actually, in momst games, multi is less demanding than solo because it involves less calculations (no AI / scripted event etc...)
Not really. Multiplayer, at least in games that require precise positioning/aiming and split second decisions, requires putting all involved computers in lockstep as far as every meaningful game object or element goes, all happening in real time with low latency. This extra synchronization requirement tends to put a far higher strain on the computer than just calculating things locally, given that waiting for the data on the objects tends to take more time than calculating that data locally would take. Add to that encryption (if you want to avoid man-in-the-middle cheats, that is), lag compensation (which involves a combination of trying to determine where every other player or NPC will be and remembering where they were in the near past), chat/voice comms, and you should see why in the past most games posted different minimal requirements for single player and multiplayer.
as for the network part, they are very very low, so low that you can't actually tell the impact it does have cpu-wise even on the lowest comp....
Very low if you think just about bandwidth. Extremely demanding when you think about latency, at least for games where changes need to be shown in real time.