The pressure is set exactly as you supposed. The injection steam has multiple functions. First is to heat the BFW to the highest temperature possible for the corresponding saturation pressure that vessel design limitations dictate. So, some of the steam is condensed as it passes its heat to the BFW. Therefore, theorhetically speaking, you could control your steam tightly, and set the pressure by putting just enough steam in to heat the water to the desired saturation temperature, and no more. Not a good idea.
The purpose of heating the water, aside from boiler heat transfer reasons, is to raise the water temperature to a point where the oxygen soluability is as low as possible. Generally speaking, 15 psig, which is 250F reaches a point where you have gotten a lot of the benefit that you are going to get, but 50 Psig deaerators are not uncommon.
But, you will notice that deaerators have devices, like spray nozzles, trays, packing, etc., that distribute the water for good contact with the steam, and hence, maximize good heat transfer.
Excess steam, over and above what is requred to just do the heating and pressure regulation, acts as a 'scrubbing' medium to get the oxygen, which now has low soluability, "liberated" from it's bond with the water, and swept away with the excess steam to the vent, where it is returned to the atmosphere. That is why every deaerator you see has a steam plume. (some do not have enough, however. Be careful) The trays and sprays, and/or packing all distribute the water in such a way as the scrubbing steam can have maximum contact with the water to get the scrubbing done.
How much turndown you require will dictate whether you go with sprays, trays, or packing. Whether or not your BFW has a lot of dissolved oxygen or not, also drives your design.
I personally speaking, do not like the idea of the coil, unless for some reason your BFW is already very pure condensate, coming from a hotwell that already has an ultra low oxygen concentration, as you don't get the type of scrubbing with the boiling off of the coil surface that you get with the methods mentioned above.
I hope this is enough to start the conversation.
rmw