We have very good examples of people raised without language, and beyond the threshold of the ability to acquire it, who nevertheless 'think'.
Deaf people in cultures who do not have a critical mass of deaf citizens to develop conventions for dealing with them like sign-language or ideograms, or methods of teaching reading as a first language mode, are numerous enough to study.
There is very good reason to believe that they think, as they can act out stories for one another and engage in something like both dramatic and comical dialog though those. But the process is extremely slow.
Some of those people can learn language later in life, but others live out their entire lives this way. Your question presupposes that they have some kind of underlying syntax, but, if so, they fail to discover it in one another. Very seldom do these communities evolve a real language. To me, if that syntax is somehow 'really there anyway' this seems unlikely, as they spend fifty or sixty years confined to one another's company in very small groups, because those with language do not have the patience to enter into their interchanges.
After acquiring language, even individuals raised this way have difficulty rejoining these groups, as the painstaking process of conveying enough detail to be understood becomes too trying for them.
So I think your conclusion is true, that language does not need to be the basis for thought.
As to the speed of precipitation being an indication that symbolic thinking is not taking place, I do not agree. The brain is massively parallel, so symbolic thinking can take place sub rosa, a little bit at a time in many different times, hidden from view. (I am psychoanalytically inclined, so I hold definite biases as to how this happens that are less-than-defensible philosophically. But I think it is still quite true.)
A thought may pass into conscious perception all at once, but you do not think only, or even primarily, or even 'more', when you are 'thinking'.