Guitar picks are a great tool for guitarists, but they aren't a necessity for every musician. Some incredibly talented musicians prefer to play with just their hands because of the feel they get for the instrument. Others use coins or other items to play. There is no right or wrong way to play the guitar, and what works for one player might not be the best fit for another.
Absolutely possible. Many folk and country players are not just good, but great, without a pick—and some rock players are, as well. A lot depends on the style of music definitely but as you can see from 'The Doors' to 'Jeff Beck', a lot of variety can be played without a pick. At the end of the day, it all depends on your command on the instrument.
The quality of play has al lot to do with the quality of the instrument that is being played, but has even more to do with the skill level of the individual playing the instrument. A skilled musician can make music from anything. I recently saw a video in which a musician made a clarinet out of a carrot. It sounded great. It is therefore not impossible to think that a guitarist can make great music using a coin rather than a guitar pick.
A guitar pick is not the only, or even the best, tool with which to play an instrument. Queen's Brian May uses a British sixpence coin, and his illustrious career is ample evidence that even the most unexpected tool can be put to impressive use. May surely has his reasons for using a coin, and no one need question him.