Yes, a series resonant circuit can induce large voltages across the inductor and capacitor. It is simple physics. The high frequency AC current routed through the inductor will result in a E = ZI kind of voltage, where Z is the inductive reactance and I is the current. This is not unlike what happens in a Tesla coil. Be careful with this voltage. I can cause RF skin burns and can fry a scope.
If you drive the series LC network with a push-pull driver, the source voltage is just 5vpp, with a 5v supply.