Yeah you are right. I guess in programming languages phonology does not have a role to play so syntax shoulders everything about expression formation. This is also true, in a broader sense, for artificial languages like Esperanto, where there is much less externalization-induced irregularity (e.g. the so-called ["disharmonic word order"](http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199684359.001.0001/acprof-9780199684359)) compared to naturally evolved languages.
The book you linked looks interesting too. I (from a traditional linguist's perspective) see quite a few directions CT may be applied to the study of natural languages, and the Categorial Grammar line of research is just one of them. In my PhD work I have been looking at another direction, and I think more possibilities are on the way now that Applied Category Theory is growing faster and faster. :-)