No, that's not right. Latin has a separate copula --- sum, est, and so on. What gives Latin its terseness is that it supports dropping words implied by context (like the copula in many contexts) and that it's highly inflected, allowing single words to communicate grammatical information that we need word spam to spell out in English.

Uh, yeah, what you said. I'm not a linguistic expert so my experience with this is just "that's what it does" rather than "you can drop copulas" ;) Another one of the nice ones is that you can drop pronouns from context too–compared to English the Romance languages are pretty cool.