But I have noticed that the verb 'to be' is absent most of the time, so would it work without it here?
I found this one is really hard to explain as there are no rules for that, I believe. It is just very natural thing for a native speaker. You can express similar things in different ways in Ukrainian, but this different ways may have different emphasis or/and be less/more formal. I think if someone asked you Там є люди? (Are there people there?) it would be better not to omit є and say "Так, там є люди." "Там люди" is more of an answer to the question Хто там? ( Who is there?) - Там люди.