I didn't find such setting. Is it even possible? I'm currently using KDE 4.14.2 (Debian testing). Is it any different in Plasma 5.x?

No, but in theory the translucency effect (it's written in Qt script, check /usr/share/kwin/effects/kwin4_effect_translucency/contents/code/main.js) could be extended to ADD translucency.

However, oxygen and some other styles used to / turn tooltips into ARGB windows and paint them translucent. This can *not* be reverted from outside the client process (ie. the application or one of its plugin like the style)