No!
I won't make the claim that it will be impossible to force a 44-40 case into some 44 Magnum chambers, but you shouldn't shoot the wrong ammunition in any arm unless you're dealing with some sort of survival/emergency situation where such a risk may be justified.
The 44 Magnum is is straight case, the nominal body diameter is 0.456".
The 44-40 is a bottle neck case, the nominal base diameter is 0.4689". Much 44-40 ammunition has a smaller actual base diameter, some cases on my shelf run as small as 0.461". Further, the 44-40 case can be as much as 0.020" longer than the 44 magnum: the potential for the case jamming in the forcing cone is present, if remote due to the case mouth diameter being 0.443" maximum. 44-40 cases may also have problems establishing a good gas seal in a 44 Mag chamber, at a minimum you're going to end up with a filthy revolver and some split case necks, at worst, you'll have to deal with high pressure gas going where it shouldn't.....
Further, in deference to older Colt revolvers, the bores of which may run in the 0.424" range, many factory bullets are substantailly below the 0.429-0.431" range of bullets used in 44 magnum arms. If nothing else, this can cause accuracy troubles.
Bob
