Can I install porcelain tile without grout joints on a fireplace?
This is more or less a matter of opinion, but many floors of many types have been installed over the years without grout. If you don't want grout, don't use grout. 

Regarding your point #1, grout isn't structural in the sense that it prevents movement. Your mortar and a sound substructure do that. It's not a valid concern.

I don't know what you're saying in point 2. You can't grout tiles that are tight together, even if it's non-sanded. You need at least a minimal void to accept the material and ensure a good bond.