If Level II for a given ticker is showing that the top ten sell orders currently displayed total 25,000 shares. Then a buyer were to enter a market order for 25,000 shares, would the order "buy up" the top 10 orders on the Ask with a corresponding increase in share price? Obviously, some of the sell orders would probably be synthetic, but for purposes of the question, let's assume that the totals showing are actual.
Yes. Your demand for shares reduces the quantity supplied at the ask price. If you purchase all of the shares supplied at that price, the next share purchased will have to be at a higher price unless a new seller comes online.