I very much doubt it, given that one of the hallmarks of language is the arbitrariness of the sign. While there are some systematic patterns (such as onomatopoeia and phonaesthemes; see http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4123678/ for a rigorous analysis), it is very unlikely that there is any langauge where all the words are considered "intuitive" to all other languages; in fact it's unlikely that there's even a single word (in any language) that the rest of the world would link to the same concept. (Even examples that stack the deck don't work out; onomatopeias and animal sounds differ quite a bit across languages, even though they are based on a sound in the real world; and words for mother and father, which presumably have a lot of similar sounds in common because they are based on the phones that babies acquire earliest, still have exceptions.) In fact, if there were a "word" that every speaker of every language in the world could readily understand without knowing the language, I'm not sure that would even be considered "language" anymore; things that have pretty much cross-linguistic meanings, like a startled shout, aren't really language (and even a lot of these, like laughter, still differ in usage across cultures).
For the most part, I tend to agree with Stephen in the arbitrariness of languages. However, some patterns that might be common in some languages (e.g. Shrieks are high pitch sounds that attract attention and are generally symbols of pain, or warnings). From these basic symbols, more evolved symbols might emerge with these "primitive" commonalities. Other limiting factors in symbol combinations are degrees of freedom in hand movement, overall range of frequencies that a human or animal might make, etc.
Overall, symbol combinations are limited to the medium and physical constraints of the generating instrument(mouth, hand, etc.). This contrasts with the theoretical formulation of language combinations that are infinite in principle. Another limitation in symbol combinations is that while symbols are theoretically allowed to be infinite in length, the capacity for a human and animal is not.
In short when making reference to languages one has to make the distinction between the concept of languages (theoretical study where they are taken as infinite and independent of time) as opposed to its actual implementation(time dependent and evolving but constrained by its underlying mediums). When talking about implementations the there are elements that are not independent given the generating instrument and medium. However, one has to be careful when attributing causality based on these limitations. There are other factors that might be taken as independent events in the evolution of languages and might be easily confused with these limiting nonindependent factors.