Southwest lost my infant car seat base that I luggage-checked, but it was okay because I knew how to install the bucket without a base (and that's how I had used it on the airplane). It showed up about 12 or so hours later.
American lost my gate-checked stroller on the way to Orlando. Took two days to show up. They gave us a piece-of-garbage loaner that wouldn't even push with my 30lb 2yo son in it. Fortunately the Disney hotel found a slightly better stroller that had been abandoned by a previous guest, and that got us around until our stroller showed up.
Yes, they will give you loaner seats, but there is no guarantee that it won't be disgusting (like the extra seats that American had in Orlando 3 years ago when they lost our stroller), expired or the right size/type for your child. They could present you with a seatbelt booster for your 1yo, or a backless booster for your 3yo, neither of which is a good idea at all.
Is there a reason that you don't want to use the seats on the airplane? If you won't use them on the plane, are you meeting someone at the other end who can just buy seats for your use on the trip? Or arrange transportation that doesn't require car seats?