Can Mt. Gox convert USD to EUR or do I have to convert it through Bitcoin myself?
Mt. Gox has a BTC/EUR market so you can sell your bitcoins for EUR and withdraw them.
But you mention that you already have a USD balance at Mt. Gox. The cost to convert them to EUR within Mt. Gox will vary based on the ask price on the BTC/USD market and the bid price on the BTC/EUR market. It is possible you can buy BTCs with your USDs, then sell them on the BTC/EUR market and even after fees still end up paying less than any other conversion method (based on the forex EUR/USD exchange rate).
However, if you simply want to do an international withdrawal, you can withdraw USDs to your bank and your bank will charge you a conversion fee to change those funds into EUR. Wire fees from Mt. Gox apply.
For smaller amounts (e.g., less than $1K USD or so), you will likely find it more affordable to buy bitcoins and sell them for EUR then withdraw as an inexpensive SEPA transfer.
MtGox doesn't convert funds. The only way to obtain USD would be to open a USD wallet, transfer the bitcoins there, and sell them. But then you have to figure out how best to withdraw the funds, which may be tricky.
If you're converting to obtain local currency for travel, consider using http://localbitcoins.com upon arrival. You'll receive cash instantly and can avoid dealing with any banks or trading firms.