A.R.
We just flew last month with our 4 month old son & kept the stroller (snap-n-go) & the carseat to check at the gate. We had no trouble checking any of the things. We did bring large black trash bags to wrap them in so they did not get banged up. We also asked if there were any available seats for our baby & on the one flight there was so we were able to keep our son in the carseat buckled into an airplane seat. When we landed our stroller & carseat were given to us at the airplane door.
Everything went well except we forgot how many delays there are when traveling now, so be prepared for that.
Happy travels!