Naruto looks like s06p when in km and even more so when in bm.
Since when in km he is ooozeing life force and minato said he sealed yin chakra it can be implied that kurama only has his yang chakra(tbb was said to be positive and negative chakra as shown here....not yin and yang
so then as you see him fuse his chakra with kuramas he looks exactly like the silolete if the so6p....(remeber kishi is a dbz fan and when dbz characters fuse they kinda fuse their traits(i think kurama and so6p did a piccolo style fusion/sealing) and naruto with kurama is similar to fusion dance...)
even without the dbz influence, he simply when fuseing his chakra with kurama looks just like so6p(aka his body) with kuramas pressumed only yang chakra....
my theory is that since it is hinted that oro can undo the death god seal that the kyuubis chakra will be released, and naruto will see 1 of 2 things 1 would be his bm would change or 2 he would be capable of some how unlocking a new mode(rikudo mode?) but the logic is if so6p sealed his soul in kurama then his knowledge and mental energy(yin) would be sealed when minato sealed the yin chakra....and his body energy and appearance would be with yang(physical)
so by getting yin chakra back naruto would gain either so6p knowledge, or would gain his dojutsu (when in bm)
its possible that he would have to have senjutsu chakra as well to gain that dojutsu, since the so6p is theorized to use sm.....
in the end i think if kuramas yin chakra is released he will not only look like the so6p but essentially become him(when in bm or higher)
he wouldnt get permanet eyes and when in base form would be the same but when he goes full power he is the so6p essentially