If I annotate a Eukaryote and I get a

proteins.faa

file, is this pipeline appropriate or is it more for screening prokaryotes?

It's definitely only been designed with prokaryotes in mind

I’m interested specifically in BGC and CAZymes. Looking at the metromap AntiSMASH I think has a fungal mode. Do you know how feasible it would be to tune some of these tools with custom databases to tuned for doing genome discovery in specific eukaryote lineages?

For antiSMASH Probably in that case you could annotate outside of the pipeline, supply the annotation files and then make a custom config for the special flag for fungal mode (is it is a single flag, I don't know anything about that mode - I thought it was a whole other software based on the dedicated web server). For other the other tools I think the databases were quite hard or not at all customisable, but you would need to check