It is a possibility. Shinigami are hinted at being able to have children, especially in the case of the Shinigami coming from the Noble Houses (Byakuya, for one, appears to have been born in Soul Society), and in one of the filler episodes of the Anime, it is pretty much blatantly stated that people are born inside Soul Society.
As Arrancars are Hollows, former human souls, who have been Shinigamified, I personally think it isn't absurd to assume that, yes, they can have children. However, considering the... harsh lifestyle of Arrancar, and Hollows in general, it is unlikely that anyone of them would actually try to have children.
However, being mainly Hollows, it's very possible that they're very infertile, and might have a very, very low rate of actually successfully impregnating someone or being impregnated. A Shinigami male and Arrancar female might have more success in trying to have children than an Arrancar male and Arrancar female, for example.
At this point, it's all speculation. No hard, solid facts about this exists, as far as I know. It is possible we might never get a straight answer to this question.
Along with that Ichigo's daddy Isshin Kurosaki was a Shinigami Captain