Apricots are pretty high in fiber which means that if you eat enough of the apricots then yes you can have a laxative effect as a result of too many apricots.
I love apricots myself but have to watch how many I eat because after I eat a bowl full of apricots then I usually start having to poop soon after or I get stomach cramps and possible diarrhea.
I once ate 2 bowl fulls of apricots before and I had the diarrhea within a few hours after so yes eating apricots can be a good natural way of getting rid of constipation and to get your bowels moving.
Apricots do have a natural laxative effect and really do get your bowels moving if you eat enough of them.
Apricots are also good at preventing heart disease, strokes etc and improve your heart health and may even prevent other diseases.
I have an apricot tree in my yard and so I have a lot of free apricots available to me and I give some to my neighbor as well.