Well, it very easily could. 1 SCU is 1.25*1.25*1.25 m. This means that 3584 SCU would take up 7000 cubic meters. Sounds like lot? It isn't. That's just a cube that's 19.13m*19.13m*19.13m. Or 19m*19m*19.4m to make it a bit prettier. Now, with BMM being 160m*160m*65m (LxWxH), fitting that sort of cube inside it wouldn't be all that difficult, even if you removed the wings and dead space from BMM dimensions you'd still have something like 80m*60m*40m (quick estimate) of perfectly usable internal space. Could very easily have like 40m*20m*10m cargo area, or make it 45m*25m*15m to make it bit more spacious with room to walk between the cargo and retrieve some containers from the back.
Other way you could consider 3584 SCU would be 16x16x14 single SCU boxes. Or like, 32x16x7 (LxWxH). The cargo hold could be divided to two columns, so 32x8x7 *2, these sides could then be divided to 4 rows, 8*8*7 *2 *4, the large containers are 2 SCU wide so having 2.5 SCU pathways columnwise would be pretty nice, rowwise I think it'd be enough to be able to just walk between them, let's say that's 1SCU worth. And you'd probably want to be able to move around them, so 2.5*3 extra space columnwise and 1*5 SCU extra rowwise. Giving a total of 37*23.5*8 (added bit space above as well) cargo area when measured in SCU boxes, or 46.25m*29.375m*10m. Round that up to 47m*30m*10m and it still fits very nicely within the BMM. Also pretty similar to what I figured when working solely with meters.
Or, were you wondering if it could be more than 3584 SCU? Yes, it could be more than 3584 SCU. We have some pictures where the cargo hold sort of expands slightly outside of the ship, if you did that I think you could double the height of the stored cargo, doubling the amount of cargo it could hold. Now, obviously they're not going to double the cargo it can hold, but it's not impossible. They could if they wanted but I doubt they will.