No, that is incorrect. Disney will NOT guarantee connecting rooms for any party because there is no way to block them. As long as there are 2 adults on the reservation, the expectation is that the adults can split up. WDW will do everything possible to grant the request, and most people do get the connecting rooms, but it's not a guarantee and you could end up in different floors or different buildings.
OP, have you looked at the family suites in ASMu? Those tend to be a little lower priced than AoA suites and you could walk to Sports. Or a cabin at FW? It looks like you are a party of 5+infant, so there are not a lot of options. You could also look into renting points at DVC. Many families your size opt for off-site; Wyndham Bonnet Creek gets a lot of good reviews from larger families.
Enjoy your vacation!