Mat promised Elayne he would see her safely back to Caemlyn. Elayne is certainly back in Caemlyn, but Mat didn't take her nor does he know. And we all know Mat Cauthon ALWAYS keeps his promises...

 

So, will Mat have to bring Elayne back to Caemlyn at some point in aMoL?

I think you're taking Mat's promise a little too literally.  He promised to see Elayne safely to Caemlyn.  Because he keeps his promises, he accompanied Elayne to Ebou Dar.  Since then, Elayne has been safely to Camelyn and claimed the throne.  Mat isn't going to show up and tell Elayne whenever she leaves Caemlyn, "Sorry, I promised to bring you to Camelyn.  You're just going to have to forget about whatever you're doing so I can bring you there."  Elayne's in Caemlyn, so his promise is fulfilled.

I think you're taking Mat's promise a little too literally. 

 

Have to agree.  Not sure I remember all the particulars correctly.  He kept her safe through Salidar & Ebou Dar (sp).  This includes the confrantation with the Gholam, etc.

 

We know there were then going to use the Bowl of the Winds, and then return to Caemlyn.  If you recall, he didn't even want to wait for using the Bowl of The Winds <remember his stare down with the Sea Folk leader?>. 

 

I remember Matt couldn't follow her out of ED because the Dice started rolling, the Seanchan invasion started, and Olver had run off.  The collapsing wall fell on him and then the Dice Stopped.  We now know his destiny required for hime to stay in ED so as to meet Tuon / Daughter of the Nine Moons. 

 

Elayne, Aviendha, Birgitte, Nynaeve, Knitting Circle, Sea Folk then went to "The Farm", used the Bowl of the Winds and then proceeded to Caemlyn.  We can fairly assume her having gotten there, and Rand's departure from the city satisfies Matt's obligation. 

 

 

The Seanchan invasion pretty much ended his returning with them.