No, not necessarily, there are 3 systems involved here (Amadeus Seating/FLY-JFE which is an overlayer/Expertflyer), and though they talk to each other it doesn't mean that at agent can be sure to get a seat. Seats can be blocked for dozens of reasons and you can't rely on EF to have full visibility on that. EF homes in on Amadeus Seating.

What does happen at T-72 (fairly precisely) is that the reservation goes from Amadeus Seating to FLY, at that point the various blocked seats such as bassinets and First row 1s may become available with agent intervention, but it won't be before then in normal circumstances. However it sometimes take T-48 before an agent can get a seat allocated, and they may need assistance from those looking after seating in Flight Management. After T-24, when OLCI opens, normally agents can't do anything more due to the aircraft falling under Airport Control. So the best window is 48 to 26 hours before departure. It is also the case that with the best will in the world an agent can't unblock a seat for some reason, even to a Prem.