Was the Baron going to skip without paying? *Spoilers*

The Baron's sole purpose for staying in the hotel is to steal Garbo's pearls to repay a gambling debt.
He also is broke, but we do see him later gambling for 000's of marks.
I assume those he owed the money to were not going to foot the bill and if he had money to stay in a Grand hotel they'd have taken that from him, so I bet he was just running up the debt and going to do a moonlight flit!