A noted outboard manufacturer with a powerful software development team once ran a comparison test between hardware compressors and their software emulations. Even with technology that is now several years old, the results were impressive. It was VERY difficult to tell which recording was hardware and which was emulation. In a properly controlled test it is likely that most people, even experienced engineers, wouldn't have been able to tell the difference reliably.
So, according to this evidence, plug-ins can sound exactly like the hardware they emulate. But that doesn't tell the whole story…
Firstly, just because a software developer is able to make an interface that looks beautifully like a battle-hardened compressor from the 1960s doesn't mean that their emulation is as good. Some software emulations are, as mentioned above, almost exactly like the real thing. Some, unfortunately, are nothing like it.
Anyone buying a plug-in emulation of a compressor would need access to the real hardware to make a realistic comparison. And it's worth bearing in mind that real-life examples of the same compressor don't always sound the same. Circuit designs change over time; components differ; age affects different units in different ways.
Secondly, but equal in importance, is that is isn't just the steady-state settings that govern the subjective 'sound' of a compressor, or any other audio processor. It's what happens when you adjust the controls. How a unit reacts to user input is just as much part of the sound. Think of a compressor or an equalizer as a musical instrument and you'll get the picture.
But perhaps it doesn't matter how good an emulation is. Most software developers of repute offer trial versions of their products. If you download a plug-in and find that you can do great things with it, it doesn't matter how close an emulation it is to any analog hardware. And if you don't like it, then if it really is a 100% accurate emulation, you wouldn't have liked the original hardware anyway.
There's a certain joy in having nice equipment, just for its own sake. And a plug-in that looks good is surely more pleasant to use than one that doesn't. But ultimately if the sound of a plug-in pleases you, and more importantly the results you achieve please your client or market, then that's all that's needed.