That the DO would give Rand access to the TP, if he suspects that Rand will use it to defeat him.

Besides that, BS pointed out that the TP destroys the Pattern. Therefore I don't see how it would mend the Pattern:

Matt: "Ok, so, what is then the nature of the Dark One’s relationship with the True Power? In other words...is he the Power or it is separate like the One Power?"
Brandon: "When people bored into his prison they were searching for a new source of power, they found him. Alright? Now, that leaves a strong implication that the True Power is the essence of the Dark One. The True Power when it is used rips apart the Pattern to rebuild it as it desires. The True Power is very destructive to the Pattern. It leaves scars on the Pattern. Robert Jordan said in an interview or maybe it was actually in the books [both, actually - Terez], when you make a gateway with the True Power you are actually ripping a hole in the Pattern and going somewhere else. When you are using the True Power that is what you are doing, it is contrary to the Pattern. That is not a direct answer to your question but I think there are enough implications in there that certain things can be discussed."

It makes more sense that Rand will use the OP to mend the Pattern (plus probably some esoteric stuff about his special blood and/or soul). If the Bore - which can be sensed in the Pit of Doom - is basically a big Gateway through the Pattern, one should be able to Unravel it, once the Seals which block it are gone (would explain Fel's musings on this topic). Note that even the nihilist Moridin, who doesn't care about death, expresses anger, when he saw in PoD, ch.2, that Aviendha successfully Unraveled a Gateway. This was considered impossible in the AoL. Thus maybe the anger actually came from Moridin considering that this would be a possibility to close the Bore.

Besides Aviendha and likely Min coming up with this possibility, maybe LTT's memories will also be helpful to figure it out for Rand, since we know that LTT was one of few people who could block a Gateway.