You can indeed play guitar without nails, but you will have a limited dynamic range. It is so much easier to push into the string to bring out a melody with a strong nail than it is with flesh.
I have heard of people doing the following (not sure about how healthy this might be). One idea is coating the problem nail with CA (crazy) glue. Another is fake nails which is essentially a chunk of acrylic glued to your nail. A third idea is using some of the commercially available delrin fingerstyle picks that mount on your fingertips. But these fingerstyle picks are aimed towards steel string fingerstyle, so I have no idea how much they would tear up nylon strings.
I happen to be lucky that my nails which are constantly trashed during guitar making all grow back quickly and strongly so I’m never without them for very long.