Technically, yes that will work. But, especially if you plan on overclocking, you want a reliable PSU. AngelOfDarkness recommended a PSU that is complete overkill for a R9 270X. One of those cards will "technically" work on a 450w psu, although you probably shouldn't do this.
I would recommend this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139048&cm_re=corsair_600w-_-17-139-048-_-Product
I would recommend that you go above the power requirment listed for your card, incase you decide to upgrade later, or if you choose to overclock.
Right now the CM600 has a $20 rebate on Newegg.