Does the output signal from the FIR filter have transient response?
Probably. Except for 1-tap filters, if your signal is of finite support, FIR filtering needs to assumes  values outside the support (before and after the values you were given)), and those values are often considered to be $0$. Hence, the extended sequence $(\ldots,0,0,x[0],x[1],x[2]\ldots)$ may produce some artifacts or transients in the output around time $[0]$, depending on the continuity and smoothness of $x$ close to $k=0$.