If the excitation of the synchronous generator fails, it acts as .?

it acts as an induction generator

 When TG Synchronised suddenly Excitation fails, magnetic coupling between Stator MMF & rotor filel will be lost.But the Turbine is delevering almost same active power.Alternator act like a INDUCTION GENERATOR, drawing reactive Power From the System. Large Slip frequency Current will induced in Rotor, resulting in Rotor Over heating, vibration will occur.

Loss of field is detected  by measuring Impedence at stator terminals.Terminal voltage start reducing & current tend to increase, Power Factor changes from Lag to lead, the Impedence locas goes in4th quardent.

For a generator to generate energy there a two fundamental requirements1) field excitation2) mechanical enegry from a prime mover. Hypothetically speaking, if the generator is  working in a standalone condition and  the exctation is cut off, the rotor of the generator will continue rotating (due to the prime mover) but there will be no electrical output. In case the generator is connected to a grid then again hypothetically speaking, it may act as a load drawing power from the grid and act as an induction motor whose direction of rotation would tend to oppose the direction of rotation by the prime mover. However, in real worl scenarios all generators would be provided with under exitation relays which would electrically isolate such generators from the grid.

it will generate random voltages and frequencies 

When the GenSet is already online and synchronized with the bus then suddenly excitation fails, then if the loss of field (or under-excitation) relay and reverse power relay fails to trip the breaker and isolate the GenSet from the bus, possibly it will act as a motor and will draw power from the bus. But if not yet online or synchronized, simply no power is generated.

it may turns to act  as a motor