The 'real' overdriven sound of a valve amp comes, not from its pre-amp, but from the power valves, which produce those pleasing overtones when pushed hard. That's why valve amps are cranked loud, if that sound is required. The only way to get it 'really' is to have a valve amp and turn it up a lot, into a very good, solid cab or cabs; this can result in shattered windows, and buggered ear-drums. In the '60s, we knew no better, but there's no excuse these days. Either buy a very good modelling amp, or use a 'Tube Screamer'-type pedal. It's much, much lighter, eats far less electricity (and so is good for the Planet...) and 'that' sound can be had at reasonable volume levels. As it happens, I'm not a fan of disto, dirt, crunch et al; I like a nice clean sound, so my valve amps don't get pushed in that way. Our 'trick', back then, to get that sound without going deaf was to put the 4x12 cab flat on the carpeted floor, speaker side down, so as to allow the amp to be turned up and not go deaf. Yes, a cranked valve amp can be glorious, in the right hands, but it's a very expensive game.
The previous answer is correct; you can't play a valve amp without its speaker load (unless it's been specially designed for that, which is rare...), and it's impossible to get 'that' sound as an input to a solid-state amp. Get a pedal; start with a Tube Screamer (the clue is in the name...). Hope this helps.
Douglas