The way to express support with a candidate is voting in the election. No other way is really needed and the voting on the questionnaire answers may not have any useful purpose other than influencing other voters. But an as independent vote as possible is probably preferred. Maybe it's because we are used to vote on many things and the software allows it.
Let's look at the data (last five moderator elections on StackOverflow). I sorted the questionnaire page by votes and then looked up the candidates final place in the election (when they dropped out or if they made it, how many percent of votes they got; primaries were ignored). This gives the election position sorted by questionnaire score and can visualize a possible correlation.
2020 - 12th moderator election
The election position sorted by questionnaire score is: 2, 1, 3, 4, 6, 5. That is a very strong positive correlation (CC=0.88 (correlation coefficient with simply increasing numbers.).
Bug: In all election pages I saw the link to the questionnaire (under additional links) is always pointing to the 2020 questionnaire instead to the right one.
2019 - 11th moderator election
The election position sorted by questionnaire score is: 8, 2, 1, 4, 5, 9, 6, 7, 10. With a remarkable outlier (the one with the highest questionnaire score only came in 8th) this is a strong positive correlation (CC=0.56).
There are some numbers missing in that list. That happens if I could not find a questionnaire for this candidate. In 2019, the third position in the election (runner-up) does not show up publicly in the questionnaire. It was deleted by the candidate. By vote score (46) it is second-to-last.
2018 - 10th moderator election
The election position sorted by questionnaire score is: 10, 1, 8, 6, 5, 7, 3, 2, 9, 4. Now that looks interesting, the candidate with the highest scoring questionnaire barely made it through the primaries, while two out of the three elected moderators had relatively weak questionnaire answers. There was no strong correlation between questionnaire score and election result (CC=-0.21).
2017 - 9th moderator election
The election position sorted by questionnaire score is: 2, 1, 6, 3, 5, 9, 10, 4, 7, 8. This is a strong positive correlation (CC=0.67) with both elected moderators also having the highest scored questionnaire answers.
2016 - 8th moderator election
The election position sorted by questionnaire score is: 5, 3, 2, 6, 10, 1, 4, 8, 9 There is a significant positive correlation (CC=0.42) but it could be stronger, the 10th in the election had almost the same score in the questionnaire than the first in the election.
There is some evidence that the questionnaire score and the election result are positively correlated (there are still the nomination pitches, which are not voted on, as well as other candidates stats and the number of votes on questionnaire is much lower than in the final elections). However, correlation does not imply causation. It's possible that the questionnaire scoring influences voters but it's also possible that this correlation is simply depending on the quality of the candidate.
We cannot rule out that the questionnaire score influences voters. It also affects the sorting order for users that usually sort by score. And I have a hard time coming up with a good reason why it's needed (after all feedback on the candidate's answers in form of a score is not desired, we want to get to know their views, not what they write after they know what we think of them). That's why for me, casting votes on questionnaire answers is not necessary.
From Delete votes on a Moderator Election Questionnaire "..there's no particular reason for anyone to vote on these answers at all - it has no direct effect on the outcome of the election. ..we tend to just let folks cast up/down votes as they please..At some point in the future, we may build in more elaborate support for these questionnaires, at which point it might be worth disabling voting" basically says it all. Maybe this feature will come at some point in the future.