I'd expect that to be negligible because the size of funds Google is already part of (QQQ, VTI, SPY, etc. etc.) are orders of magnitude larger than ETFs that track the Dow (DIA is the only one that comes to mind).

The Dow itself is a bit of gimmick in that its value is the sum of all the prices of the stocks in the index. Meaning if Google joins at $120 but kicks out a stock that was $300 then the Dow would go down 180 points.

No, it wouldn't. The Dow is weighted for exactly this reason: https://en.wikipedia.org/wiki/Dow_Jones_Industrial_Average#C...