Dropsync is a two-way automatic sync client. It will sync file additions, changes and also deletions from your Dropbox to the SD card in your phone and vice versa. It is meant to be a configure-and-forget tool. Once configured Dropsync would stay in the background and does its job according to user settings. This is very similar to how Dropbox client works on PC and Mac.
It is safe to pair a local folder with a Dropbox folder even when there are existing files in both. Dropsync will recognize which files are the same on both sides and link them together without uploading/downloading.
In normal day-to-day usage the amount of data changes is usually small. Dropsync tries to be very efficient in detecting changes. The CPU time spent and thus battery consumption should be pretty minimal if there are no changes which would cause files to be downloaded or uploaded.
You should go to System settings and set WiFi sleep policy to Never. WiFi sleep mode doesn't save battery that much, it slows down network connection and causes Dropsync to keep the CPU awake longer.
Dropsync tries hard to avoid causing catastrophic data loss. In the worst case, even if you run into an unknown serious bug in Dropsync you should always be able to log in Dropbox website and restore the lost files from history.