Has anyone tried to servitorize a Tyranid before? Like, just a little hormagaunt. Would that work?
Tech-heresy via the illegal mixing of human technology and xenos aside, not really.
Firstly, servitorisation is a specific process that requires, as far as we know, a degree of sentience to enable the undertaking of specific tasks and programming routines. You need those cognitive processes and that capacity for comprehension there to make the servitor serve. A gaunt, separated out from the Hive Mind, is basically just an animal. An alien animal. While we have plenty of examples of mechanical animal familiars and cybernetically augmented pets, we've never seen much in the way of a true animal servitors (cyberarachnids, some rats, some dogs) because, as far as we know, it typically wouldn't work properly or have any point, and is very hard.
This is part of why servitorisation is so fundamentally sinister; it specifically relies on taking something with memories, thoughts, comprehension, and using those things to make an effective slave.
Additionally, even if you did theoretically servitorise it, the moment the Hive Mind touches that gaunt again, your technology doesn't count for shit. We have seen attempts to control Tyranids, and they simply don't work once the Hive Mind reconnects with the bioform. Not only that, but it also makes the Hive Mind aware of your location which, y'know, not good. Hell, we've even seen that the more localised influence of a Genestealer Patriarch can override the programming of infected Skitarii.
Good questions, though!
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