Kindof. The mere fact that the S&P 500 exists causes the potential jump in price for that one stock, but since you hold everything in VTSMX, you also see the jump in TSLA.

Worse, since you own every stock (not really, but close enough), you now have the 500 companies representing about $27 trillion of market cap, and then thousands more representing only another $8-9 trillion. So any change in the smaller companies is dwarfed by one good (or bad) day of AAPL, AMZN, GOOG, etc (as happened yesterday).

So if you want the whole stock market, buy it in multiple pieces - a large cap, a small cap, and a mid-cap funds.

As to your bookkeeping comment about being easier, you are absolutely correct. In fact, a competent financial advisor has the tools to trade the S&P themselves for clients (literally buying all 500 stocks individually and in correct proportions to the index).

Market cap source: https://siblisresearch.com/data/us-stock-market-value/