But the market cap of bitcoin will not rise X because X value is put into it. It will rise Z when X value is put in.
Price goes up when buyers buy more than sellers sell. It has *nothing* to do with "incoming" money. Market cap is meaningless.

At the risk of uttering a tautology, exactly as much bitcoin is bought as the amount that is sold.
But we are talking about the chaotic dynamic relationship of price, first of the digital asset in the legacy system, and then transforming into the legacy system emulated over the digital asset. This is where all the opportunities come from...
But yeah, also 1btc=1btc.