If the a'dam prevented a non-channeling Dreamwalker from accessing Tel'Aran'Rhiod, it would indicate that abilities not reliant on access to the One Power are indeed stymied.

Otherwise, all we have seen is that physical movements and the use of the One Power to remove it is denied. In fact you can use the One Power to explore the a'dam without the Power being impeded, implying that the collar houses a Binding that works similar to the Three Oaths.

We've basically never seen a channeling Dreamwalker collared because none of the Wise Ones have had to deal with it and access to T'A'R itself is not dependent or connected to the One Power, while having access to the OP bolsters certain abilities there.