UJT firing circuits for SCR
No. Since there are no random components in that circuit and it is fed from a constant DC supply it should perform exactly the same on each cycle.

If you want random firing you need to introduce some further circuit elements. Given that you're probably looking for low frequencies you could use a small micro or a pseudo-random sequence generator.



Figure 1. From Clabacchio's answer to https://electronics.stackexchange.com/questions/30521/random-bit-sequence-using-verilog.