I have a 580exII and sometimes feel limited by the line of sight required to use it is a slave with the on-camera flash.
Will a 600ex-rt's radio control feature work with my 70D, or will I need to buy the radio transmitter too?
Yes and no.
So far (Sept 2014), no Canon bodies can trigger the Wireless 600EX-RT flash via RADIO. However, a 70D can trigger it via OPTICAL (ie flash pulses) method, same as a 580EX/430EX etc.
So, you must attach a radio transmitter, either a ST-E3-RT or another 600EX-RT, to the 70D in order to trigger the 600EX-RT via RADIO signal.
While this essentially duplicates what you can do with the previous optical technology, using the RT devices does give you some additional features: your 70D can set all configurations for the 600EX-RT via its menus, and the coolest feature: you can trigger the camera remotely from a 600EX-RT (called Linked shooting). Whether this is worth the extra expense (at this time) is up to you.
You'll also need to buy an on-camera transmitter unit, such as the ST-E3-RT or another 600EX-RT to use the radio communication. Yongnuo makes clones of the Canon RT gear: the YN-E3-RT, and the YN-600EX-RT, as well as a YNE3-RX receiver to integrate manual lights and older Canon TTL (menu-commandable) flashes into the RT system. Shanny also has a clone of transmitter, the SN-E3-RT, but have not yet come out with their 600EX-RT clone.
You could use the optical master in the 70D's pop-up flash to master a 600EX-RT optically, but this is pretty much the exact same system you're using with the 580EXII, and will suffer from the same limitations.
There is also a less expensive and system-restrictive path to take, which would be to get 3rd-party radio triggers and use those to trigger the flashes remotely instead. They range from very cheap (typically manual-only, though--so you can only tell the flashes to fire, and you won't have eTTL, remote power control, or high-speed sync) to more expensive TTL/HSS-capable triggers, to very expensive but super reliable/robust professional triggers of either variety. One good website for researching radio triggering flash gear is the Flash Havoc website.
However, the Canon RT system, while it is the most expensive and the most restrictive system also offers the most functionality. With a post-2012 body (which the 70D is), you also gain (over the old optical 580EXII system), Groups D&E, Gr(oups) mode--which lets you turn groups on and off individually, as well as mix groups that are under Manual, eTTL, and MULTI modes, ID codes (essentially giving you thousands of discrete channels to avoid interference), and the ability to control the camera shutter from the flash. The 600EX-RT also has several usability enhancements over the 580EXII, mainly centering around having a dot-matrix LCD display which allows for "soft" buttons/menus that are less cryptic than the UI on the older flashes.
Whether those new features are worth the additional cost vs. using radio triggers is up to you. Syl Arena created a series of videos on the differences between the 580EXII and the 600EX-RT for Canon Europe's CPN site that are well worth watching to get a feel for how the two models differ.