The original question actually mixes two different, though related, topics: (i) making a recording with just synthesized instruments and voice and (ii) using MIDI to control synths.
If the question is, "Can you make a recording with just synths and voice?" the answer is obviously yes. I'm pretty sure there are several whole genres of music that consist of nothing but that, sometimes without even the voice. The trickier issue, of course, is what happens once you get out of those genres. Rough-hewn acoustic folk music is probably going to sound a bit funny. Standard-issue radio pop, not so much of a problem. I'll agree with the others on the subject of guitars: generally you're going to do better with an actual guitar. I don't know if that's because it's hard to synthesize a guitar, or just because everyone in the world knows how to play a guitar, so there's no market for a good synthesized imitation anyway. With other instruments that are supposed to sound like, you know, instruments, the quality of the soft or hardware and taking some time to get the parameters and variations right can make a big difference.
If it's, "Does using MIDI to run the instruments destroy everything?" the answer is generally also no, so long as the synth sounds right. If it's something electronic that's ordinarily played with a keyboard (like, say, an organ) it doesn't even know whether someone's pushing keys in real time or a computer is telling it imaginary keys have been pressed. On the other hand, if everything lines up perfectly in time, there's no variation in velocity and there's no timbral variation or expression, it's can wind up sounding dead.
Bass should work fine, at least outside of some genres, like popping/slapping funk or something. Entire records have been made with all the bass lines played on keyboards going back to the '60s. If a keyboard can play it, a MIDI sequencer can.