But standard FDM printing will not get you keycap that are smooth on the top, as they tend to be sculpted to fit a finger better, and you're still looking at ~0.4mm layers at best. You may be able to do it with SLA 3D printers which are able to do higher resolutions than FDM printers.
Yeah, you can 3D print key-caps reasonably easily. Sorry, I can't remember the exact 3D model, but there's a free Cherry MX switch model around somewhere that surprisingly has the entire interior mechanism modeled. You can pull out the key mesh and tweak it a little bit to meet your needs, then it prints really well and fits nicely on Cherry (or Gateron) switches. There's also a handful of pre-created 3D printable keycaps on Thingiverse, however when I last looked into it I wasn't very happy with them.
Although, I must admit, whilst I've had all my components (including RGB LEDs and transparent Gateron switches) for what must be over a year now, I still haven't gotten around to finishing the project!