I am by no means an openings expert, but I have played the Slow Slav as White for a long time so I will just make some comments.
In general, lines with an early b7-b5 in Chebanenko positions tend to work better with a Nc3 than a Nd2. As you have already noted, a Nd2 makes it much more likely that White will be able to find some way to exploit the holes on Black's queenside (particularly c5, a5, and c6, often exploited by a well-timed a2-a4) created by an early b7-b5. Positions with b7-b5 and Nb1-d2 are not necessarily very good for White, but they do seem to give a better chance of White gaining a small advantage than the main lines, and a small advantage is usually the best that White can hope for against the Chebanenko these days. Positions with a Nc3 make it much more difficult for White to exploit the holes Black makes on the queenside with b7-b5, and give Black more dynamic compensation for such holes due to the possibility in many lines of a well-timed b5-b4, forcing the Nc3 to an awkward square.
Since an eventual b7-b5 is the general idea behind a7-a6, I always respond to 4...a6 by playing Nb1-d2 (either right away, or more commonly a little later after Bf1-d3). This is probably White's best try for an advantage in these lines. If Black goes ahead and plays b7-b5 anyways, I generally get the kind of position I want, which I would describe as lightly +=.
However, if Black refrains from playing a quick b7-b5 and plays something like an immediate Bc8-g4 (say, after 4...a6 5.Bd3), he still has a very solid Slav position in which the "wasted" move a7-a6 is compensated for by the fact that d2 is not an ideal square for the White N in lines where Black does not play b7-b5 (that is, because it removes some of the pressure from d5 and because in some variations the Nd2 can also get in the way of the Nf3). Typically, in positions with a strong center like this (pawns at c4/d4/e3), White would prefer his Ns on the most active squares, c3 and f3, where they simultaneously pressure Black's center and support possible pawn advances by White. So the move Nbd2 after a7-a6 may also be viewed as a kind concession.
I like to look at the exchange as a kind of exercise in prophylaxis: Black plays a7-a6 as prophylaxis against White's ideal set-up in the center with Nc3; White then plays Nb1-d2 (or just refrains for committing the N to c3 for a while) as prophylaxis against Black's idea of b7-b5. Black, having now discouraged White from playing his ideal set-up with the N on c3 (I use the word "discouraged" very loosely here because positions with Nc3 and b7-b5 are fully playable for White), then plays Bc8-g4 with the idea that this set-up is even better after the exchange of a7-a6 and Nb1-d2, because a7-a6 does not hurt Black and the Nd2 is slightly misplaced. White is not entirely convinced of this last point, because Nd2 is at least a developing move, while a7-a6 is not. And so the discussion continues, with White trying to find lines in which his Nbd2 is actually useful.
As far as I know, there is no clear way to an advantage for White in lines with the Nbd2/Bd3 set-up against a7-a6, but the play is different and less forcing that the positions with a Nc3. Having played many games with this set-up and a number of games with the main line Slow Slav positions (that is, with an immediate Bc8-f5 or Bc8-g4 instead of a7-a6), I would evaluate both set-ups as roughly the same: +=/=. They are very slightly easier to play for White, but White has no significant advantage if Black knows what he/she is doing.
The upshot of all this is that 4...a7-a6 appears to be fine against the Slow Slav set-up as long as Black refrains from an early b7-b5 before White commits his N to c3. In such positions, the move a7-a6 once again proves to be a high-class waiting move, with a dollop of added prophylaxis.