RC time constant - theory vs practice (simulation)
An RC circuit generates a T=RC delay to a threshold of (1-e)/e, or about 0.63 of the original step. If you trigger at a different threshod, you will get a different delay.

Your threshold appears to be the 0.7 V Vbe of a silicon BJT. If the battery voltage is much higher than 1.1 V, perhaps 3 or 5 V, then the delay to 0.7 V will be much less than RC.