Logically, he must know immediately whenever someone attempts to draw on the True Power, because a) it's now been confirmed the DO is the True Power (BS confirmed LTT was right about this) and b) Jordan has always said having access to the True Power is a matter of the Dark One letting you access it, and no special connection between you and the DO need be established first.

In a similar way, the DO knew whenever the Taint (which was confirmed by RJ as being the TP too) was filtered back to him, and so he knew whenever a male Forsaken channelled saidin (before the Cleansing).

So it's not a matter of going to SG and getting permission, it's a matter that Shai'tan lets you use the True Power or not when you try to access it. It's one important reason why the Forsaken freak out about using it and believe Moridin is mad to have become addicted to it: one minute you have access, the next time you try to access it the DO might decide to cut you off.

So, access is probably known instantly by Shai'tan whose essence is being embraced (and by who most likely as well, since the DO can descriminate between who he lets use it and who he refuses to let use it), but does the DO know exactly what you weave with his essence afterward? Maybe, maybe not. We don't have tons of clues, but if we look at what happened when LTT touched Shai'tan/The True Power to seal the Bore, or what happened at SL when the two streams of balefire touched (and what happened totally baffled Moridin), it seems there is a trend there, and that trends seems to be that the Shai'tan may retain a certain amount of control over the TP at all time. In other words, what you weave with it may work as you intended only because Shai'tan lets it happen, and if he so wishes, the weave might transform itself and do something else. In the case of the SG episode, contact with the OP let Shai'tan "climb" all the way back to the True Source before LTT and the others released the source, ending up with a certain amount of TP "imprisonned" there, which became the Taint. In the SL episode, it seems the True Power piggied back from Rand's balefire weave all the way to Rand's and Moridin's souls, bonding them in a way similar(yet different, to what extent exactly we don't know) from the warder bond. In both cases, it seems quite possible the True Power demonstrated "a will of its own" - ie: Shai'tan's will.

Personally, I think it's most improbable that Rand was able to tap the TP via Moridin. It would imply their connection to the True Source (necessary to channel the TP as well) have fused - and this obviously would work both ways. So far, there's not a clue that Rand feels anything whenever Moridin channels (he would feel it, if their connections have fused it would be like Rand embraces the TP everytime Moridin does, and Moridin would feel it too whenever Rand embraces saidin). So far, it seems the bond between Moridin and Rand is most similar to the bond shared by Elayne and Birgitte (ie: a same sex warder bond). Like Moridin and Rand, Birgitte and Elayne have shared physical sensations in a way the warder bond doesn't normally allow. Their periods have shifted to follow the ecaxt same pattern, when Birgitte gets drunk Elayne acts drunk and she shares her hangovers, Birgitte shares Elayne's pregancy's incomfort. Their mental links also go deeper than is normal between an AS and her warder, eg: Elayne knows a lot more about Birgitte's emotions etc., and often they mirror each other's emotions and moods with and even without realizing it. A male warder rather gets jumpy because he gets a sense that his AS is nervous, not the way it often happened to Elayne, that she would angry or impatient for no reason (it's scratched to the fact she's pregnant) before she realizes it's actually Birgitte and not her who feels this way. All in all, that's extremely similar to the bond between Rand and Moridin, who also mirror one another the very same way, both about the physical and the mental/emotional aspects (it means Moridin is gonna really, really hate that bond very soon, with post-epiphany Rand. He's gonna get like a "live feed" of Rand getting better and better and happier etc. and this all while Moridin sees his recent strategy to cause emotional harm and despair to Rand crumble in his own head. It will be funny to see Moridin gets pissed off because he's actually furious about what's going on but can't help but feel happy or full of love or hope for no good reason!)