There has been a bit of variation in 44-40, both long ago and more recently. The old standard was for a nominal 0,427 bullet. A case sized for 0,427 bullet does have a slight "step" between neck and body of case. Most modern 44-40s use 0,429-0,430 bullets and that ""step" is much less, making 44-40 more of a tapered case cartridge than anything I would ever call "bottleneck". Generally, diameter of head area on 44-40 case is larger than 44Mag chambers, so, most likely a no go.
Another area where 44-40 is different than 44 series of straight-walled cases in neck. 44-40 brass has thin necks, typical of BP-era rifle cartridges (such as 38-40, 32-20, 25-20 etc.), 44 series of straight-walled cases have rather thicker brass, typical of BP-era revolver cartridges (such as 45 Colt, 44 Colt, 44 Russian, 41 Colt, etc.).
Although, should 44-40 factory ammo, loaded with 0,427 lead bullets, be fired in a 44 Mag chamber, expect severe leading as powder gasses lead by the undersized bullet. This in common with 0,427 lead bullets fired in 44-40s with 0,429-0,430 cylinder throats and bores.
Niklas