The February 2026 crisis around the Strait of Hormuz redirected global supply chains towards the overland routes of Eurasia, and demand for the Trans-Caspian International Transport Route rose within days to an unprecedented level. This article assesses how much of that demand surge Azerbaijan's transit infrastructure was actually able to absorb. The hypothesis is that the binding constraint in the Azerbaijani segment of the corridor is not a physical shortage of fixed infrastructure but the transhipment node where the maritime and rail legs meet, together with weak border and procedural coordination. Drawing on official reporting for 2019–2026, the study applies the minimum-link principle, capacity utilisation ratios, Little's law from queueing theory, and an absorption elasticity indicator proposed by the author. In the first half of 2026 dry cargo carried across the Caspian grew by 34 per cent while east–west rail transit grew by only 12 per cent, which indicates accumulation at the Alat node. An absorption elasticity of roughly 0.03 confirms the limited short-run capacity of the corridor to convert demand into throughput. The article proposes a Corridor Resilience Index and outlines three scenarios to 2030.