Garry,
I am not familiar with the Austrian legal system, nor how they translate the names of their courts. The trial-level courts in the state of New York, for example, are the New York Supreme Courts.
Do you see this thread here:
http://www.dnforum.com/showthread.php?t=28431
Notice how a case from the New York Supreme Court in Manhattan was appealed to the Appellate Division? The word "supreme" does not have any particular legal meaning across systems, and certainly not across languages.
That is why in my note above, I requested correction to "an Austrian court" which, subject to my bothering to care about the Austrian legal system, is the most accurate thing I would venture to say about the position or authority of this court, if any, in that legal system.
Assuming for the moment that this was litigated in a trial level court and then kicked up on appeal over the issue of whether WIPO fees are a permissible line-item of compensatory damages then, yes, that is a perfectly acceptable question for an appellate level court to decide.
You cannot have ANY case tried in civil court and have a Supreme Court decide on punishment or costs - true or false?
Again, assuming that by "Supreme", you mean an appellate level court, your question here mixes apples and oranges. Appellate courts do not determine the "amount" of damages, but they certainly determine, as a matter of law, what kinds of things can be included in a damage calculation.
I'll give you an example. In the State of Pennsylvania, if I intentional inflict emotional distress upon you by shredding your favorite teddy bear, then you might go to court and win a trial award of $10 for the bear and $500 for emotional distress. However, if the trial record shows no evidence of a physical manifestation of that emotional distress, then I can certainly get the $500 component of that award thrown out on appeal.
Additionally, I strongly advise you go look up the meanings of these two words - remittitur and additur - both of which can be a basis for appellate review.
But, getting to the overall point, if it is possible for you to assume that anyone is ever liable for trademark infringement then, in an action subsequent to a UDRP, why shouldn't the Plaintiff be entitled to recover the cost of the WIPO proceeding? After all, along with lost profits and all of the other various measures of damages, the cost of recovering the domain name certainly counts among the cost of the infringement to the trademark owner. It's a no-brainer.