If I'm pretty much confident of the transparency of 192 kbps encoding of stereo music, how much more should I add to that if I want to encode a multichannel album with the same resulting quality? That is, by what should I multiply the bitrate I use for 2 channels if I have 6 of them? x3? Or is it non-linear?

The "x3" value is being used in some cases ( 64kbps HE-AAC stereo -> 192kbps HE-AAC 5.1 ), but transparency isn't linear.
Concretely, since 128kbps is usually transparent, the x3 may apply to that value ( so 384kbps for 5.1).

Can't give a better answer, but the new nero version has improvements on the multichannel encoding, so that may change things anyway.

Can you have VBR across all channels? So when its needed the bits are there and when its not its lowered to save space.

Doesn't x3 bitrate for 6 channels mean zero multichannel optimization? These are not isolated channels with entirely different data to each have a full x1 bitrate allocated, after all. They usually contain a great deal of originally identical data which was only spatially distorted when recorded from different microphones (or when engineered into front and surround channels), don't they? Such slight difference should be quite compressable, I guess, while, of course, inversely proportionate to the amount of "original" data in surround channels (like truly channel separated instruments).

If I remember rightly, AAC works using CPEs (Channel Pair Elements) so the only coupling you get is between pairs.. L/R FL/FR RL/RR or maybe depending upon the encoder, possibly more naively than that..