What's the use of onions in teriyaki sauce?
Soy sauce, sake or mirin and sugar are the usual ingredients in a teriyaki sauce. The rice wines in particular are vital for an authentic teriyaki flavour.

So the question is somewhat moot: onions aren't usually found in teriyaki sauce anyway. The onions naturally add flavour to your marinade: if you like it, leave them in, if you don't, take them out. The onions won't have any major chemical effect on the marination process.

Personally I would ditch the olive oil, replace it with toasted sesame oil and add garlic and ginger for a more rounded and authentically flavoured East Asian marinade.