AFAIK, there is no auto-Advance in the Import Dialog window. Like Mark, my goal is to get the import process started with as little effort as possible. I rarely de-select images since they can be imported faster than I can decide to uncheck them and focus my attention on the Previous Import collection in the LR Library. As I said earlier, I never wait for the import to finish before I begin my task of culling And as you have noticed, there are more tools at your disposal in the Library module.
If you insist on culling before import, the space-bar and right arrow toggles the check and moves to the next thumbnail. I have a Bamboo touch pad with 4 programmable keys. I have these programmed for {X}{Next}, {P}{Next}, {Next} and {Z} This if for quickly evaluating image in the Library. I suppose if I wanted to program a key for {Space}{Next} you could do that. Also with OSX in {System Preferences}{Keyboard & Mouse} pane, there’s a tab for Keyboard Shortcuts where you can assign any shortcut you like to any application listed. You might try that to see if it meets your needs.
It is always useful information for those of us trying to answer questions to have your user profile completed. Had you not posted the screen shot showing a uniquely Mac menu, I would never have known to suggest using the OSX Keyboard shortcuts.