1) I think Dante, and the others in this thread, speak of using smartphones/ipods as backup devices. That makes sense, something that works, is small and lightweight, as opposed to hauling around pre-amp, power amp and effects. And much more cost effective.
2) I fully agree with Dante, the magic comes from the fingers. Not the amp. Years ago, a fellow guitarist I knew, made a statement "All amps are crap. Just make the best of the amp." I am not a great guitarist by any means, only average at best, but I have almost always had other guitarists come up and ask about what I was running for tone. Whether pure tube head, tube rack gear, or modeled.
3) You can get a great sound, but the one thing you won't get is the same feel. To me, that is the hardest adjustment. When it comes to modeling, I can get the sound I want, laying back, dialing back, sure it's a bit different, but that is easy to adjust to. The harder part to get used to is the different feel. Nothing feels like playing in front of a cranked stack like playing in front of a cranked stack. But then again, playing my V-Drums feels nothing like playing real drums. Sure, I have mesh heads and such, and the physical part of hitting with the stick and kick pedal feels close, what throws me off more is the acoustic feedback you actually feel, is very different. That is what is the hardest to get used to. And personally, I think getting used to playing against that, is the bigger difference in tone. You just have to adjust.
[EDIT] FWIW, I do not play regular gigs any more, I only sit in or fill in at times, and I have little to no control over what my stage sound source is these days. That has left me with going completely with modeling and in ear monitoring, and I am used to that. I do miss being able to sustain with feedback, I might look in to something for that, but now that I am used to it, not a big deal. It took some adjustment though.