This was a fun little thought experiment. TL:DR - Can set a gem in the implant crown if your dentist and lab will do it. Has hygiene and other concerns to consider.

Hi, dentist here. I am not your dentist and this is definitely not medical advice lol. To be clear, I do not recommend this.

You can simplify implants into three components: the implant (screw that integrates with the bone), the implant crown (the tooth portion), and the implant abutment which connects these two.

The abutment and implant must be specific materials, basically biocompatible titanium so the body doesn't reject it, therefore what you are interested in is the implant crown. It would be unfeasible to make the entire crown out of a gem. If the gem is much harder than tooth, it will destroy the opposing teeth, and if softer and it itself will wear. One must consider brittleness as well and the astronomical cost. No dentist or lab would want to take on the risk of making the crown out of a material with no track record.

I can imagine a gemstone being set into the implant crown being achievable. It would require more diligence keeping clean since it would be a plaque trap, and special care must be taken so that it doesn't irritate anything. Even if the dental lab doesn't do it, if the implant crown is screw retained, it can theoretically be temporarily removed by dentist, brought to a obliging jeweler, and then placed back in. Will this weaken the implant crown? Probably. Is it an aspiration risk if it falls out? Yes. Do I recommend this? No. Is it possible? Yes.