"They started eating."
Translation:Eles começaram a comer.
No, I don't think that would be correct.
To sum up the explanation in the later Gerund lesson (https://www.duolingo.com/skill/pt/Verbs%3A-Gerund): The Portuguese gerúndio (verb form with "ndo" ending) corresponds to the present participle in English (verb form with "ing" ending), in indicating the progressive or continuous aspect of an action. In English grammar, the term "gerund" also has to do with the present participle, but it refers specifically to using it as a noun, such as in "They started eating". This usage does not exist in Portuguese, and a verb infinitive is used instead, as we are learning in this lesson.
The auxiliary verb to use with a gerúndio is typically a conjugated form of estar, although certain others are also possible, e.g. continuar, ficar, and vir. The dictionary entries for these words would specifically mention such a usage, with possibly a distinct meaning from other usages of that word.
So, we might encounter a sentence like "Eles continuaram comendo". (Notice there is no "a" in front of "comendo".) However, although "Eles começaram comendo" looks like the same construction, "começar" is not one of the special verbs that can be used as an auxiliary with a gerúndio.