I'm not sure how the search works, first of all. However, for instance let's say a beginner wants to ask about the word/verb "kakeru". Well more often than not, he will write it in romaji. If he's an advanced beginner, he might it in hiragana. Now let's say that I've already asked a question about "kakeru" but wrote it as: 掛ける. As far as I know, the beginner won't pick that up in his search. And may end up asking a question which is similar or the same as I mine. And if it is closed, the beginner is penalized as well (correct me if I'm wrong on this). So the point of this question is: If I ask a question should write out the kanji and hiragana or kanji and romaji or even hiragana and romaji, so that that another person can search or see that this question has already been asked?
I think that question overlaps with two previously tackled on topics:
The general consensus is that, while it is perfectly fine to ask questions with romaji, there is an expectation that everybody on JLU can manage kana (if you are serious about learning Japanese, there's just no way around it).
Therefore, all it takes in your example is for you to ensure that you use both kanji and furigana, and it will pop up in any reasonable search (kana or kanji). If you absolutely must use romaji in a question/answer, I would heavily encourage the use of both kana and romaji (however redundant) to avoid your post not coming up for people searching with kana.
If someone asks a duplicate question because they didn't see the same question using a different script, chances are the new question will be closed as a duplicate of the original question with a link pointing to the original question to redirect future visitors. There's no penalty for asking a duplicate question like that (unless it's a bad question).
In fact, the duplicate system is how StackExchange points people who searched for different terms towards the same question.
I asked a question about sake in romaji which had a similar question using kana or kanji (can't remember which). As far as I can tell, I wasn't penalized for it.