Can Vivaldi open tabs in the background?

Yes. Rightclick on a link, and instead of choosing Open in New Tab, choose Open in background tab, which is 2 items down in that list.

I always open a new tab in background by clicking the mouse wheel. Tested on Vivaldi right now.

Same as most browsers, Ctrl/click will open a new tab behind, Ctrl/shift/click will open in front. [Cmd on Mac]