No, maybe, yes... Almost everyone who has hosted them has lost money, but it gets your city and country in the international news, and it could be good for tourism, and it is normally great for propaganda in the host country as they normally have enough people entered that they will win gold medals.
Apart from the excellent points Korvo One made, we also get improved infrastructure. Transport, roads and venues continue to bring benefits long after the Games are forgotten.
Then there's the intangible benefit of self esteem. Anybody in a city that has successfully hosted the Olyjmpics gets a very real boost to the morale and that can spill over into other areas, like productivity.
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