If you log into your Admin account in BallotBox, and click on your active poll, the Summary tab will tell you have many voters there are, and how many ballots have been cast. There is also a graph that shows you how many ballots have been cast over time, and you can see on that graph each email reminder that is sent.
If you click on the Voters tab for the poll, you can see the status for each voter. If you click on the Status filter, you can see which voters have cast a ballot, which logged in without voting, which were invited but did not click the emailed link, and which were not invited (because of a bad or missing email address).
However, not one (not even BallotBox personnel) can see any partial results, nor how any voter voted*.
*If you specify that a question must be non-anonymous, once the poll is closed and unlocked, you will be able to see how individuals voted on that specific question in the poll results.