Yes, you will cause the network to be more expensive to use while you sustain the attack, and you will spend money to do so. The miners will collect these fees. They will be happy and invest in more hardware and raise the price, thus increasing your cost for new coins. Everyone gets richer while you waste away money.
The refutation is made by simply reading the code or the documentation regarding the TX fees. If you pay fees, so will others, and if they pay more you don't do anything to the network.
Please also look at https://blockchain.info/, I see 771kb/3000kb used in the last hour. You would need to increase the TX frequency 400% to affect the speed of lowest fee paying transactions.
Also answer yourself, why hasn't this happened yet? Surely someone is bored enough to have over 1000 BTC and no brains and simply troll everyone. You think you are smarter and more informed than everyone else? Is this an original idea that the world has never seen? Well?
This did happen on other less intelligently designed altcoins. The solution? Simply change TX fee rules, get miners to update, attack vector completely annihilated.