Hello Gentlemen,
Not necessarily. Some would say staying out of it shows some integrity regardless of whether the vote would have any influence or not. In some of the nomination polls for Best Agency and Best GFE I made I stayed out of nominating anyone though some members thought there wasn't any reason to handle the issue that way. I never had any connection to working for orhelping out with anything to do with any agency, I just thought it would be cleaner, to use one word, to stay out of the process. I did vote later in the official poll as I had declared I would before the nominations were set. Overall I guess it doesn't matter either way IF one is not connected with any bias to whatever the poll is about. Still, maybe staying out helps with perceptions of honesty even if it's not necessary.
As for public or private polls, obviously there's always an issue of bias and/or shilling. Many know who those people are and public polls allow members to discount anonymous fake ballooned numbers.
Cheers,
Merlot