I would NEVER use a modeler live in my original rock band. To me, there is nothing like a wound up Fender tweed or Marshall style amp reacting to your playing. And those amp sounds are what inspire me to write the songs for my band. It's the sound of the rock and roll that I love. And, none of the amps that I use live are that heavy, especially with the cart that I keep in my car. The amps I use live are just loud enough to get a decent clean sound that works with the acoustic sound of the drums.
That said, I have one pedal board for my original solo acoustic shows where I have all the songs programmed, and I use a HX Stomp for all the time delay stuff, and even some dirt, and it works fine. But I run my guitar through an acoustic amp before it goes to the PA.