Yes and no, I guess. Technically, no, because prizes cannot be calculated dynamically using a formula. In other words, you can't set a prize value to "3 * numberOfEntries", for example. You must set it to a fixed amount (or percentage), but no variables are allowed.
You definitely can use the automatic prizes feature to work around this, but it could also be a pretty painful exercise depending on how many players you typically have (although it only has to be configured once). I won't go into details on customizing the automatic prizes because you can find all the information on how to do this in the user manual. But you would basically need to create a prize level for every amount of players you could have. In other words, a prize level for 2 players, a prize level for 3 players, for 4 players, for 5 players, etc. Since the amount of the bounty prize would change with every additional player in the tournament, you can't have prize levels for a range of entries - you have to have a prize level for each number of players.
The <prizes> token will update with the proper recipient of a prize that is a bounty on a random player when the prize is awarded, but does not display the name of the random player on whom the bounty rested.