Actually you can, albeit that GIP will give you the same weird results as the regular Vanilla graphics. But for the coming release we're working hard on getting COREd graphics in (we won't be finished by a long shot, but at least we're working on them). We do plan to have a 'CORE in color' add-on as well as an official B&W CORE graphics pack, and the color setup will be complimentary to GIP. So we will use many if not all of the GIP backgrounds and such, but will get the CORE-specific graphics in by installing those into the CORE moddir. Apart from that we will install dummies in the regular gfx game directories, but only if no images with the same number are present (CORE has a lot more techs and models, and thus more bitmaps - and HoI will only load those which have a corresponding file in the regular game directory).
So not only will the 'CORE in color' graphics pack work together with GIP, but GIP and regular vanilla should work too without problems. Furthermore the GIP and CORE dev teams have agreed to co-operation, so we're allowed to use GIP graphics for CORE, and the GIP team can use our work if they would like to do so as well.
The first CORE graphics pack is being tested within the 0.30 beta, and as such is already available. For now it contains mainly tech imagery and tech team imagery, but we try to get as many of the other graphics in as soon as possible. Just give us time - the techs alone are 600+ images, and finding matching graphics in both B&W and color (if possible) is quite a feat. If you have imagery you'd like to see included yourself you can always PM me, as I'm coordinating the graphics efforts.
I hope that answers your question!