I've never witnessed it or attempted it, but it can be done. It's all about choosing the right mic for it along with the right acoustics. Another alternative to that is the Ampeg SVX plug-in. It has many amp/head combos along with mic modeling on the cabinets that can either be placed on or off-axis. It's just like running it through an amp and it gives a great sound. I use it all the time, and even run keyboard bass through it.
I don't think I answered your question. All I can say is have at it, and watch your frequencies, levels, distortions, and clipping. Oh, and you want to compress it to so that room noises are not picked up.