Let me preface this by saying this is all just opinion. I don't think there is any evidence that proves it conclusively.

Here's a quote from RJ:

Q: Is it possible to go to the Dream World in the flesh, and take something with you out through the gateway?
RJ: No.

As I understand it, anything that exists in the Real World and is reflected in TAR (whether it's a door knob, pickle, or someone who has dreamt himself there) is, in effect, insubstantial in TAR. That is, there is nothing substantial to be brought out, because TAR is simply reflecting their substantial Real World existence.

Could the TAR dreamer make a Gateway to the Real World? Maybe. But he couldn't step out into the Real World through it. Nor could someone else create a Gateway to TAR, and take the TAR dreamer out with him.

I think the only substantial things that can be brought out of TAR are substantial things brought into TAR by people who enter in the flesh (RJ's quote above doesn't apply to this situation - if it did, people who entered TAR in the flesh fully clothed would come out naked). So, if Rand stuck a door knob and a pickle in his pockets, and entered TAR in the flesh, he could leave those items there, and later go back and bring them out again. Because while in TAR, that's where those items EXIST - they're not reflections, in that case.

But a TAR dreamer doesn't exist in TAR, he exists in the Real World. What's in TAR is just a reflection of what exists in the Real World. Yes, that reflection can construct what he looks like, channel, and do other cool things in TAR, but he cannot create flesh for himself by leaving through a Gateway, regardless who made the Gateway. He can only return to his body in the Real World.

Regarding what Moggy did to Birgitte ... Birgitte's soul EXISTED in TAR (she wasn't simply reflected there, like a TAR dreamer), so Moggy was able to yank her out, and somehow that act created flesh for Birgitte. But that's a different situation from a TAR dreamer, IMHO.

My two cents ...