Besides the fact that no human being has a definition for consciusness nor a clear definition for what exactly would be "intelligence" (so in a way to be able to measure it in stuff around us, say dolphins or LLMs).
It's fairly intuitive that LLMs are already super-intelligences, and if they don't stay "alive" continously, is just a matter of design. We could be one simple - as in bash - "while (null) do, done" of having a thing hardly distinguisable from AGI (even if it's not AGI, whatever you can get out of that "I" letter to precisely define it as being a real one or not).
I'm sure most super-powers are already peaking a sight into the most confidential information inside OpenAI, DeepMind, Alibaba, Meta, whoever has these things running and keeping the details hidden from the general population.
For I, I'd do it, just in case some wacko start to run some of the things inside a while loop, giving some kind of ability to retrain itself and/or access to the real world (Internet access or worst, ability to control drones to physically interact with the non-digital environments).