As others have said, yes, that's mostly the case.
Even parsing C and elaborating it to a correctly typed AST is not quite as simple as others are making it out to be, though. Getting all the implicit type conversions correct is not completely trivial, and is a popular source of bugs (see some examples in http://www.cs.utah.edu/~regehr/papers/pldi11-preprint.pdf for instance).
There are also some annoying ambiguities in the grammar and in name resolution rules that mean that sometimes it's not easy to tell whether something is supposed to be a type name or a variable name: https://jhjourdan.mketjh.fr/pdf/jourdan2017simple.pdf
C is a "simple" language in many senses of the word, but it has a lot of complex details. It's fine to gloss over them when writing a compiler for a language very similar to C for learning purposes, but getting everything just right for actual C is tough.