Ich finde Deinen Vorschlag sehr passend und genau. Auch möglich:
-- See? What was the problem?

"well, what do you know? (I am allowed to go in)"

This expresses mock surprise and I think effectively conveys your sense of minor triumph in being allowed in to the room after all.

Another possible alternative here:

"well, there you go"

I agree with schnödel and rob_oz and I think that 'Na also, geht doch' can be used and in fact is commonly used to express that sort of minor triumph rob_oz refers to. I'd still like to offer another example:


A (struggling with his English homework): Oh no, I really can't do it, I don't understand it. It probably is just too difficult for me!
B: Look, you know you have to that homework and I am sure that you can do it. You are a bright kid, after all, right? Look at the question once more.
A: Ah! Now I get it! ...
1.) B (to A): Na also, geht doch!
2.) B (to himself): Na also, geht doch!

Here the expression 'Na also, geht doch', if directed at A, has an encouraging ring to it. It could be paraphrased as something like "See, I knew you could make it!"
If directed to oneself (in such a situation as depicted) it could mean something like: "Finally he made it. I knew he could not be THAT stupid"

Greetings :-)

@Raja: I like your suggestion. However, I'd replace "make" with "do".
"See. I knew you could do it."

That really sound as sarcastic as the German "Na also. Geht doch!"