Wicc
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Sometimes it's critical, sometimes it's not. If you have limited funds, aggressive guards, and can't rely on building Hydras (hopefully you can manage to build the rest), then you can safely skip a turn or two.
That's why on XL templates, I often see players upgrading Lizards (they need to spread out, break through in all directions, eliminate enemy units, etc.), while on CM templates, the priority is a slower and more methodical game.
Currently, on TE, perhaps the strongest strategy for building up around a Swamp is to upgrade Lizards on the first turn and then, before the end of the week, build Hydras with a Castle without Bulls.