The BSA Service Sheet 205 indicates the engine unit can be removed from the frame without removing major components, other than exhaust and carb. Fine if you want a hernia and busted knuckles. To dismantle into manageable lumps makes more sense, juggling is bad for paintwork and your health.
My take is that the clutch/mainshaft nut is easier to undo and tighten using the rear brake to hold the chain still, box in gear, easy to play with the nut. Barrels are easier to replace with the motor held still, safely in the frame rather than balanced on two bricks and a tin can. Putting a plunger engine and box back takes some fine hand/eye coordination, and the lighter the unit is, the easier it will be. From experience check the gearbox lower mounts screw in nice and easy first, rather than when you're down in the dirt.
Swarfy