The answer is yes. However, they don't have 'immortal' souls. The definition of the word 'soul' according to the theological aspect is 'that which gives life'. The soul is the animating and vital factor which leaves at the time of death.
Humans have immortal souls.
A 50 year-old (people years) apparently homeless black lab,
run down in the street,
drags his po' self to the sawbones,
an' lays down quietly on the flo'.
Not only does he have "soul", he's ready to sing the blues.
Humans have short, brutal existances, then nothing.