TL;DR: Compatibility between GT101 and the Tiger II hull is plausible engineering-wise, but every physical installation on record for both the Sla.16 diesel and the GT101/Porsche turbine happened in a Jagdtiger, not a gun-turreted King Tiger.
Sources
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Kay, German Jet Engine and Gas Turbine Development 1930-45 (Crowood, 2002), p.157-158 — primary technical account of GT101 development and the Panther/Jagdtiger installation decision.
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Tank Museum, Bovington — “Gas Turbine Jagdtiger” (Fletcher)
Tank Archives: Porche’s X-shaped engine
2. If this is to prove anything concrete we need more information
Documentation on this is thin, Thinner then the Sla.16 if anyone has archival sources (BIOS Final Report No. 98, “German Development of Gas Turbines for Armoured Fighting Vehicles,” is known to exist but I haven’t found it digitized anywhere), drop them here and if you have any information to add to this please drop it below.
3. The Sla.16 parallel of hull contradiction stories
The in-game Tiger II (Sla.16) is often cited as precedent, but it has the identical documentation problem: some sources (WT wiki) claim it was tested in a Tiger II, others (Tank Archives, Tanks Encyclopedia) call that a myth and say the real test vehicle was a Jagdtiger, since Nibelungenwerk built Jagdtigers in-house and it shared the same engine bay. So Sla.16 isn’t proof Tiger II got engine swaps historically, it’s the same disputed pattern repeating.
4. Historical parallel to other cases
Similar hull/variant mix-ups exist elsewhere per example the T-34-88 was dismissed as a myth for decades until an archival AFV registry entry confirmed it, and the Raseiniai KV-1/KV-2 identification has long been disputed. Worth keeping in mind that documentation gaps ≠ proof either way.
My un-asked opinion on this?
As much i am biased towards wanting a Tiger II with 1150hp current evidence only supports the Jagdtiger case, Yes in gaijin logic the Tiger II (H) GT101 could be added since the contradictory mess of the sla.16 exists already, But honestly don’t know.