From what I've read there is insufficient data to answer this. The number of known cave drawings is quite low and there is no evidence that different 'tribes' had any sort of agreement about them. Its hard to know how you would recognise that such a thing even existed. The tribal groupings would have been quite small back then, no real tribal nations nor do we any insight into any languages on a regional scale.

Secondly most of the drawings are of real world things, buffalo, emus, deer etc. Thus understanding them requires merely knowing that a bison is a bison. There are some early abstract markings that may be a 'drawing' but there is some speculation on the matter.

So, overall then yes, there's no reason why one persons drawing of some hunters chasing a deer would not be recognised by another person for what it was on a cognitive scale, but there is no way of knowing if this is true. Its entirely speculation but someone, somewhere in the past may have drawn the first picture of something, like an animal, and seen it for what it was, whilst others stood around going 'but thats just marks on a rock, what does Ugg mean its a beaver?' ...or... they might have said 'oh wow, it DOES look like a beaver, how clever is that'. We dont know and never will.

As for a 'universal code', again you'll never really know, I suspect that the idea of drawing caught on quick in the modern mind, but theres no way of knowing if that is so , and thus a need (or indeed the ability to transfer) for a 'code' on how to draw and what it means is improbable.

Eventually the change did come, so making a painting of '3 wolves running' eventually altered to a drawing that meant 'you owe me 3 sheep', but now we're no longer on cave art and on the origins of writing.