Any index fund (ETF or MF) with a replication methodology would have to follow any changes to the underlying index (S&P 500 or any other index) but some ETFs or MFs may use an optimization or sampling methodology and would not necessarily have to follow such a change, particularly if the change was in a name with a very small, almost meaningless, weighting to a particular stock.
That said, even funds that must replicate its underlying index have some degree of flexibility around when they make the changes by buying or selling stocks based on index changes. The manager may have a period of a few weeks over which to make the trades so that not all the index funds following a particular index will be in the market at the same time buying/selling the stocks going in/out of the index. Index changes do appear to create some degree of volatility around the stocks going in/out of an index but the degree can vary greatly based on a number of factors such as the liquidity of the stock, index weighting, $AUM tracking the particular index…
In the well-followed indexes, most people know what’s happening and most of the arbitrage is taken away. That being said, it’s usually beneficial for companies when their stock enters an index because there is natural demand for their stock from index holders.
However, here’s an example from the last S&P 500 index addition on June 30th:
Stock: WDC
Weight in S&P 500: 0.0733%
Average Daily Trading Volume: 5M shares
Shares traded on 6/30: 50M shares
% Price Change on 6/30: 0.04% (up 1 penny from 26.49 to 26.50)
Conclusion: 10x the amount of volume, but not much price impact.
Hope that helps you, chrisc.