Yes, I use the Panasonic 12-35mm f2.8, 35-100mm f2.8, 7-14mm f4 and 25mm f1.4 with my E-M1 and all the distortion corrections are applied, but you do need to check the CA removal box, and in some extreme cases with the 12-35mm f2.8, I have even needed to use the purples slider to remove excessive fringing beyond what the default correction does.
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The correction profiles for geometric distortion and lateral chromatic aberration for Micro Four Thirds are stored in the lens, and the corrections are applied directly by the camera to the live view stream, video and JPEGs, and embedded by the camera into the RAW file. Both Panasonic and Olympus cameras honor the distortion correction, only Panasonic cameras and the E-M1 and E-M10 honor CA correction (which is dealt with just as well or better in Lightroom anyway if you tick the CA correction box for automatic correction). The next step in RAW is that the converter honors, usually without any other option, the correction profiles embedded in the RAW, and this will be true of any mainstream RAW converter.
http://www.dpreview.com/forums/thread/3708551