Sort of. I've heard hi-rez needledrops that sound remarkably like vinyl. When I get a little more time and space, I intend to pick up a pro ADC so I can rip my favorite vinyl to 24/96 digital. I still love physically using vinyl, but it would be nice to have a digital backup of everything, too. Maybe I could figure out a way to get 24/96 digital in the car - that would be amazing.
As for faking tubes, well, in some applications. For audio, a big part of the "tube" sound is putting tubes onto output transformers. Solid state tends to have a low output impedance, so solid state amps tend not to need output transformers. However, if you put output transformers on solid state, I suspect you'd get more than a little of the tube sound. McIntosh built some solid state amps with output transformers - I haven't heard one, but would really like to.
In other applications, you can't quite mimic tubes. Guitar players love tubes because of the way they distort when overdriven. Solid state distorts in an entirely different way than tubes do and there's no way to mimic that, other than maybe sampling tube distortion and playing it back. Also, tubes are great for high power linear RF amps, used for radio broadcast. Tubes handle high voltages much better than solid state will.
But for audio applications, yes, I think you can get close to the tube sound with solid state. But why would you want to? You can have a much simpler circuit and if you use common tubes, they will always be available. Solid state chips go out of production after a few years then become impossible to find. If you have a problem with solid state a few years down the road, you'll never be able to fix it. But I can still get tubes and every part I may need for my Scott 350B FM tuner, which was made in 1961. That's a major reason I stick with tubes - I hate to throw out something because it cannot be repaired. For me, solid state gear is disposable. I won't spend much on it because it cannot be repaired, just sent to the landfill or cannibalized for parts. Tube gear, however, can be kept working for decades. That's where I'll put my money.