Need to make sure Thyristor switches off with rectified AC
The capacitance in that circuit won't affect the turnoff characteristic of an SCR.  An SCR will turn off whenever its anode current drops below its holding current. 
Check a datasheet for the Ih of the SCR device you are planning to use.  If you can't find a datasheet on the SCR, you can generally safely assume a maximum holding current of several mA for small devices, and 200mA for devices rated 10A and up.

As long as your rectified AC source actually can reach a 0V potential, with a resistive load, you shouldn't have any issues with the SCR turning off.  Even a simple reactive load shouldn't have any trouble turning off, since the effective voltage across the device would go reverse polarity as the reactive load dissipates its stored energy.

If you are working with very low power loads, you also need to make sure that the load will achieve the latching current of the SCR.  Typically the maximum latching current (Il) is about twice the holding current.  If you are trying to turn on the device, and it won't stay on, you need to increase your load.