Can I take my baby home in this car seat?

I have the Safety first grow and go 3-in-1 convertible car seat. I’m getting induced Sunday and have had a couple people tell me I need an infant carrier car seat or they won’t let me leave the hospital... this car seat is good from 5-50lbs and literally advertises “good for the first ride home from the hospital”. It does not have a detachable carrier. If we need to get a rear facing only seat, I’ll have to send my husband to the store before we leave but I’d rather no surprises and I wanted to use this one solely because of its safety features and now I’m worried they won’t let me because I don’t have a carrier. I’ve been told they want to see the baby in the carrier that snaps into the car seat holder.