Or in other words, does the lens correction do ANYTHING if i only shoot in raw?
In terms of the images themselves, all it does is set flags in the metadata that DPP recognizes, and it would then apply those corrections on your computer. If you use another RAW converter, then the in-camera corrections will not do anything to the RAW image. They will be applied to the JPG preview image that's embedded in the RAW file, though, and it's that JPG that you see during image review on the camera (and also the histogram data, although lens corrections shouldn't affect that, Picture Style, ALO, etc., do).
I tried to verify that DPP made the corrections based on flagged settings, but could not confirm that with my 5D MK III. Corrections were turned on in camera, but DPP did not apply the corrections to the raw files.
I manually applied them, and then the size of the cr2 file more than doubled after I saved it.
The corrections were applied to jpg out of camera images without any noticible increase in file size.
Two different things being discussed and need further clarification ...
1. Basic lens correction
Corrects for vignetting and chromatic aberration. Supported in-camera for JPEG or through DPP software as post. The same corrected JPEG is also embedded to RAW, if shooting in that mode, as well as being flagged.
2. Digital Lens Optimizer (DLO)
Advanced correction using sophisticated reverse optics transfer algorithm. Supported through post-processing using DPP software and only compatible with RAW files (no JPEG). Optimization data is non-destructive and appended to the original RAW file, which may more than double in size. For that reason, it is transparent to third-party RAW processors (e.g. Adobe Light Room).
Note, it's not possible to use both 1 and 2. The two are mutually exclusive.
OP and Neuro was referring to #1.