No. Ważny != poważny.
ważny, ważki = important or still valid, lit. having big weight
poważny = serious (no emotions), important (about: problems, ideas etc) but with humans it means showing no emotions or poważny kandydat - a real, serious candidate (one that can win, that has support), ważny kandydat is only important judging by some rule.
In another sentence from this lesson, "Mój brat nie uważa, że to ważny człowiek" → "My brother does not consider him an important man", the pronoun "to" seems to be translated as "him". But for this one, "They understand that he is important" is not accepted. Is mine a possible translation, or am I missing something?
The reason why he isn't accepted here, is because ważne is neuter and can't refer to a person. Also, a noun is mandatory here if you want to refer to someone or something specific that hasn't been mentioned in the previous clause. Without a noun, you must use the verb 'być' and it will refer only to the subject of the previous clause.
(1) Mój brat nie uważa, że to (jest) ważny człowiek - My brother doesn't think that he (not he himself, but someone else) is an important person.
(2) Mój brat nie uważa, że jest ważny / że jest ważnym człowiekiem - My brother doesn't think that he (himself) is important person.
(3) Mój brat nie uważa, że to (jest) ważne - My brother doesn't think that it/this is important.
Instead of (2) you can also say "Mój brat nie uważa siebie za ważnego człowieka".