Traditional NLP has long held (supervised) syntactic parsing necessary for\nsuccessful higher-level semantic language understanding (LU). The recent advent\nof end-to-end neural models, self-supervised via language modeling (LM), and\ntheir success on a wide range of LU tasks, however, questions this belief. In\nthis work, we empirically investigate the usefulness of supervised parsing for\nsemantic LU in the context of LM-pretrained transformer networks. Relying on\nthe established fine-tuning paradigm, we first couple a pretrained transformer\nwith a biaffine parsing head, aiming to infuse explicit syntactic knowledge\nfrom Universal Dependencies treebanks into the transformer. We then fine-tune\nthe model for LU tasks and measure the effect of the intermediate parsing\ntraining (IPT) on downstream LU task performance. Results from both monolingual\nEnglish and zero-shot language transfer experiments (with intermediate\ntarget-language parsing) show that explicit formalized syntax, injected into\ntransformers through IPT, has very limited and inconsistent effect on\ndownstream LU performance. Our results, coupled with our analysis of\ntransformers' representation spaces before and after intermediate parsing, make\na significant step towards providing answers to an essential question: how\n(un)availing is supervised parsing for high-level semantic natural language\nunderstanding in the era of large neural models?\n