Cherry Picking The Diamonds From The Stock Market

Since stock index funds buy the same stocks as the index, won't their prices become artificially inflated?

My understanding of the DOW or S&P500 index funds is that if GE represents say 1% of the S&P500, it will represent 1% of the value of the S&P500 index funds.

Since many people invest in these index funds to represent the market, won't any company in the index be artificially inflated in price due to heightened demand?

Another way to ask this is: Do companies that join an index experience a bump in share price & do companies that leave experience a drop within a short amount of time?

Thanks!

"Another way to ask this is: Do companies that join an index experience a bump in share price & do companies that leave experience a drop within a short amount of tim"

Yes, there's a well known "index-effect". There's even a bit of a game of trying to guess which companies will be added to the index.

Companies are deleted from the index usually because of acquisition, or bankruptcy. Very rarely are they "just deleted", so a "deletion effect" is less common.