Is brush-on Mod Podge the same as the spray can variant?
So in terms of the formula used in both versions, they are pretty much the same. The slight difference in the spray version though are to account for the spray version needing to be thin enough to spray through the atomiser. 

The best choice of which to use for your particular application, comes down to the mediums you used to repaint the doll, its curing time and permanence, and the potential for the ingredients in each product to react with each other in a "beading" or "repulsion" manner. 

I have some questions:


Is the paint you used on the doll water or oil based?
Does the paint you used have a specified "curing" or drying time?
Is the final item going to be placed around infants or pets?


The reason I ask that last one, is that if there is no specific concern that a baby will be putting this in it's mouth or something like that - I might recommend a light, quick spray with a clear satin finish acrylic spray lacquer first, just to set the paint, in case a layer of mod podge does make the paint colours bleed. 

ALSO!
Do a quick stress test.
paint a spare piece of wood with the doll paint and test out if sponging it on affects the paints final look.
Good Luck!!