Clap relay using 555timer - not sure about voltages around transistor
Your assumptions on how it works are correct. However this is a poor design because it is critically dependent on the current gain of T1. 

The BC847's HFE can be as low as 110 or as high as 800. The 'A' version is more tightly specified at 110 to 220, but even this narrower range could produce wildly varying results. With HFE = 110 the steady state trigger voltage will be about 1.8V (above the threshold), but at HFE = 220 it is about 0.2V so the 555 will be continuously triggered.     

To ensure that it worked with any BC847 you would have to either choose a higher value for R2 that covers the full range of possible HFE values, select the required value on test, or make it a trim pot that is adjusted to suit each individual transistor. 

The other alternative is to change the circuit to make it less sensitive to HFE variations. If R2 is connected between the Base and Collector of T1 then the Collector voltage will tend to stabilize at around half the supply voltage, and the circuit should work with a wide range of transistors.