Do orders actually execute at market price when trading high enough volumes?

If you were to start with an account of $1 mill and swing traded stocks (no options, futures, etc) ONLY intraday on 1 minute charts with a strategy where you're aiming for 0.5% to 3% profits on the full account per day, how likely would it be to actually execute a trade at the market price (both buy and sell)?

For example, let's say I'm looking at TSLA and see that the last 5 minutes the close for each of those minutes was $123, $122, $121, $120. If I buy at market on the sixth minute with my full account of $1 million (~8,333 shares), and the stock is at $119 at 55 seconds into that sixth minute, would it execute and fill at $119? Then, after 20 minutes the stock is at $125, and I execute a sell order for all shares at market, would it execute and sell at $125? If not, would it be better to use limits?