Interesting idea, but, no, it wouldn't dry the bag much. As others have commented, you need the moisture to GO somewhere else. With heat and no air flow, you will evaporate some of the water, but that water vapor will only travel to a colder, distal layer of the sleeping bag and condense there.
I know from much personal experience (smuggling frozen seafood across state lines) that even a few layers of fleece are impressively effective at keeping hot or cold food hot or cold for hours. The inside of the stuff sacked sleeping bag would still be warm 14 hours later, but only warmer, not dryer.
To dry a bag, get it into the sun. It is impressive what that 1 kWh/square meter sunlight will do. And, with the bag open, you get the ventilation you need to evaporate the water from the warmed bag. If it is cloudy or rainy, or you need to get hiking, stuff it and hike. Watch for sunny times through the day and drape it over a rock at lunch or over you pack as you hike.
This makes me wants to calc the output of those iron-salt-water-wood shavings hand warmers and report it in watts. It is obviously vastly less than a 100-watt bulb. Ballpark: about 5 watts? A sleeping bag in the sun can potentially absorb much of the 1000 watts of solar energy landing on it.