Grips for a 5906 will fit a 3566 -- GENERALLY speaking. That's to say if you are talking about the OEM delrin 3rd Gen 5906 grip, yes, basically the same with the extremely slight difference in that the 3566 makes use of a detachable magazine well and you may need to trim the small bit on the bottom end of the grip exactly where the grip pin fits to accommodate that magazine well.
In the interest of full disclosure-- I am basing my answer on the ASSUMPTION that a 3566 Limited is very similar to the 5" PPC9 that I have.
To go a bit further...
There are some aftermarket grip options that made use of the frame cutouts in the grip area where the magazine is visible with the grip off and my PPC9 does have a slightly different configuration in this area specifically (and I would guess the 3566 Limited does as well) and any grip that locks in to this area would need to be modified to work properly, but it isn't rocket science.