Are CORS Issues Possible?

tl;dr

No.

Detailed Answer

With the default module configuration, you won't have to deal with CORS issues. useKql and $kql pass given queries to the Nuxt server route /api/__kirby__. The query is fetched from the Kirby instance on the server-side and then passed back to the client. Thus, no data is fetched from the Kirby instance on the client-side. It is proxied by the Nuxt server and no CORS issues will occur.