Not really. It might make the price per coin forever lower, but market cap is determined by how many people want to buy the coin, and how much money they're willing to put in.
If 100 people are willing to pay $1000 for a coin, it's market cap will be $100,000 -- regardless of the supply of the coin.
Look at how DOGE used to be in the top 10. An individual DOGE is worth almost nothing, and the supply is unlimited, but it is way ahead of '42COIN', of which there will only ever be 42.