Hello there,
I think it's a great idea to have a support at home for the first 3 weeks. I would accept that offer only if I knew that this person would do major housework (cleaning, cooking, serving food, washing up, laundry, sorting laundry, shopping etc.) Because that's what I would mainly need after giving birth. I gave birth to 2 lovely children that both were born via emergency cesarean. With our first child we had no family support at all (they all leave abroad) so me and DH were left to manage everything on our own. I was in a lot of pain after c-section and caring for a newborn was very hard. Hubby was on paternity leave for 2 weeks so was helping as much as he could but we wished we had some extra help from family or anyone else really because we were exhausted! I wasn't sleeping because was feeding on demand and hubby was taking care of home (cooking, shopping and so on).
With our second baby, we thought that we needed that additional help as we learned from our experience. So my MIL came over and was staying with is for 1 month which was great because she was taking care of home and also looking after our toddler, who was only 2.5 that time. Thank God she stayed with us because unexpectedly I had another EMERGENCY cesarean and birth complications! So I had to remain in the hospital for almost 10 days and I was in peace knowing I have a support at home, DH was with me in the hospital as I needed help, and MIL looking after DS and home.
I was breastfeeding so I was co-osleping with my DD and I didn't need any help with looking after the new baby apart from just someone else holding her for a while so that I can eat or have shower or play with my toddler.
Having said all that, yes, I would strongly advise you to take an offer of that extra help! But I would insist that person would mainly take care of home and not the baby cause the mother knows best how to take care of her baby. Yes, the nanny can show you how to bath the baby or how to change the nappy, or how to position the baby when breastfeeding (or how to bottle feed, prepare formula, and sterilize bottles, if your DW chooses to bottle-feed) but all this will be explained in the hospital by midwives and nurses. You don't need to hire a nanny to show you all this. Just ask the midwives and they will show you.
All the best and good luck with everything.