Isolating fan noise from analog circuit
No, your circuit A is susceptible to electrical noise generated by the fan. However, the amount of noise generated by the fan, and how much it would affect circuit A are not clear. A possibly greater concern is that circuit A is supplied with an unregulated voltage source. Circuit A may implement it's own voltage regulation, or it may not need voltage regulation, but in your schematic, it is subject to significant ripple. The filter capacitors remove some ripple, but a significant fraction will remain. A voltage regulator inserted between the filter capacitors and circuit A will dramatically reduce both power supply ripple, and any noise that might come from the fan.
Inserting a linear voltage regulator, which would be cheap and easy, would involve some voltage drop between the filter capacitors and circuit A. However, if you could tolerate the ripple, you could probably tolerate the voltage drop. Also, if your transformer is rated 24VAC, that refers to rms value, not peak. When 24VAC is rectified, it gives more than 24VDC peak output -- more like 24*1.4=33.6V. That is not the average DC output, nor the lowest given the ripple, but the peak. So, if you need 24VDC output, a linear voltage regulator should not be a problem.