It might be possible, but it surely isn't easy nor obvious. "Instantly," as you claim? Sorry, but I'd bet a sizeable stack of money that's not the case. Perhaps if you're talking about a 20-year-old 1st generation Line 6 Pod or Yamaha Fx500, then okay, I can see that. But modern modeling amps are exceedingly good at reproducing the nuances of a valve amp. The Kempler is remarkable -- I would go as far as to say astounding -- in its ability to reproduce the breakup, compression, warmth etc. of an amp at all volume levels. If you heard one in person you'd be a believer. At the other end of the spectrum, even a $150 Fender Mustang amps does a respectable job of sounding faithful [disclaimer - the factory settings are pure rubbish and almost embarrassingly poor, but tweak the settings in the computer editor and a whole wealth of sounds are available, some of them are brilliant).
And why would someone want a valve amp for playback of recordings? The same reason you claim to hear the "warmth" of a valve guitar amp. The same reason guitarists use an EP3 (echoplex tape delay) with the tape out -- that preamp circuit compresses, clips, and enhances the waveform in a way that is very pleasing to the ear. Some notes increase in clarity and bloom in a pleasant way.
A valve amp doesn't imply distortion. Leo Fender was a radio tech before forming his amplifier/instrument company. He knew the value of having lots of headroom.
The key is blind testing. Everyone thinks that they can tell the difference between a Kemper and a valve amp.
I've posted many threads over the years at TheGearPage, with real amp recordings vs hardware/software modellers, and in nearly all cases, the guesses are just that - guesses, which fall into a 50/50 distribution. That is of course, when the guys who are purported 'experts' actually participate in the polls. Most of them tend to disappear whenever they are challenged to voice in on them.
I have some lovely tube amps here, and I also own a couple of Axe-FX's, and for me, when travelling, the Axe-FX is my 'go to' purely for convenience. At gig volumes, and in a band mix, it is pretty hard for me to tell the difference, and I enjoy the tone the same.
I know a lot of guitarists say that they have to have the 'feel', but for me, the 'feel' is there anyway (I usually feed my Axe-FX through the power amp stage of a real amp). I normally play fairly clean, blues/rock based stuff, and the last gig I flew across the country for, the rented backline actually had a Mesa Rectifier III for me. I've never played a Rectifier style amp before, but I had my Axe-FX, with a Fender Bassman amp model preset, through the power amp stage of the Rectifier, and it sounded amazing. The other bands were asking me how I was getting such crystal clean tones out of a 'metal' amp!
The ode to the way things used to be I think drives this market. Combine that with vinyl and you have a medium and listening experience that's superseded entirely.
Audiophiles... I don't understand why you want tube amps. They are good for guitar players because of their imperfections (e.g. overdrive, "warmth", etc) which is the last thing I want when I'm listening to a quality recording.