For long term storage, that sounds a terrible idea. Do you really want to trust your savings to $20 of electronic components that aren't designed to last more than a few years?
Yes. Ideally, only money you should have on the exchange is stuff that you are moving around often. If you're trading you don't have a choice, but if you're just holding why not use a wallet you setup?
Unless your local security is worse than that of an exchange