Is the stock's price at any given moment the price at which all shares could be sold to new investors?
No. For the simple fact that the current bid/offer always have sizes associated.
What you should be looking at is the consolidated price to buy/sell X shares (10bn doesn't really work as not everyone is willing to sell/buy).
If you look at the spread of the consolidated price at your quantity level, you'd notice it would be in stark contrast to the spread of the best bid/offer but (by definition) that would be the price to buy or sell X shares to new investors.
Edit
Calculation of the consolidated price of X shares: You go through the order book and calculate the size-weighted average price until you covered X.
Example:
bids 1000 40.00 1000 39.80 1000 39.60
So the consolidated price for 3000 shares would be $39.80, the consolidated price for 2000 shares would be $39.90.