Correct there, but increase the value of C10 to something like 470uF to 1000uF, 25V. you are now drawing more current through the positive half of the circuit, to power the fan, so the ripple voltage there will be higher. The voltage at the fan will be around 14-15V, so, depending on the fan and how much current it is using, a series resistor on the fan power might be needed to drop some voltage, so the fan is not going to overheat the internal coils, or be noisy. For a typical fan of 12V 100mA, around 10R 0.5W will do, and then you can add another capacitor (100-220uF 25V) after it to your GND point to reduce electrical noise from the fan being fed back to the rest of the power rails.
Depends on the transformer and what you are powering as to how good this will be, but as this is going to power analogue circuits probably a good thing.
Alternatively you place the bridge rectifier on the AC1 input and the GND, and treat the output as floating, and use a 1000uF capacitor to smooth it, and connect the fan across this supply directly, or via the second capacitor and 10R 0.5W resistor. This at least leads to the lowest DC component in the power transformer secondary, making it run cooler as it is not having a constant DC ( the half wave rectifier effectively means the transformer has a nett DC component applied to the core) offset pushing the core further into saturation on one half cycle.