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Depends on the formula(e) it uses. Most probably no.
Keep in mind that the whole ICE-T stuff is just fudging a pressure-measurement into a somewhat useable airspeed guesstimate. It's severely limited, but so far it's the best shot we have. Also, several steps in the ICE-T conversion-process are actually useful (CAS and EAS) for load-calculations as that's basicly what the aircraft "feels" in terms of pressure-distribution. So it's not totally worthless...

CAS to EAS involves a ram recovery factor to account for compressibility and EAS to TAS takes air temperature into account. You can squeeze that into a relatively simple formula.
When you're going supersonic, though, there's not only the stagation/ ram rise at the entry of your pitot tube, there's also a shock-wave in front of it with a pressure-differential (density-, temperature-differential) accross the shock.

In subsonic flow you're measuring total pressure versus static pressure and then figure out a Mach number by taking a fancy formula and entering those two values and the ratio of specific heats (which is 1.4 for anything slower than hypersonic). That Mach number can easily be converted to TAS by knowing OAT.

In supersonic flow, that measurement is spoiled by the normal shock-wave in front of the pitot tube, which causes a total-pressure loss and hence inconveniently falsifies your measurement even more. Also, it's hard to solve analytically and you'll need tables to find an answer. Check the Raleigh pitot tube formula and you'll see what I mean. You could figure out the Mach behind the shock (normal shocks always compress to subsonic => use the subsonic formula). Then you can figure out the Mach before the shock via a table/ formula.
In any case, the way of determining TAS would then be similar to "subsonic":
You'll solve for Mach and then you'd try to go via OAT (which is harder to do than subsonic, as "OAT" is measured behind the shock, which of course gives us a false reading - thanks to another shock table and the Mach-number before the shock which we just figured out, we can figure out the temperature ahead of the shock, though) and work out your TAS.

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