When you say, "eligible for President's Circle" what exactly are you referring to? Do you mean if you book this class, can you not pick up the Fullsize Elite Pickup Truck they assign to you and instead choose a different vehicle from the President's Circle section? If so, the answer is, maybe. It depends on whether the location will allow it. Sometimes they will, sometimes they won't. Typically, they require you to book a midsize, standard, or fullsize car in order to choose from Ultimate Choice, but they may still let you do it.

Note that President's Circle (PC) is just the highest status level of the Hertz Gold Rewards program. While you can choose from the PC section of Ultimate Choice, it doesn't confer any other benefits in terms of vehicle selection/upgrades other than that.