I am mining with a RX 470 GPU and a Intel 6600k CPU on Win7, would I get a higher hashrate mining using Linux OS?
You can't say in general, since it depends on too many factors like exact hardware configuration, OS distribution and version, driver version eg.
From my experience, you will get slightly better results with GPU mining on Windows than on Linux. This is mainly because of much better driver support for modern GPU chips on Windows. However, if you are very familiar with Linux and tweaking, building your own binaries eg. you can probably get even better results on Linux.
But: I would just give it a try and install the latest Ubuntu build (to get the latest drivers) on a separate partition and benchmark it against your Windows results.