With the R-44 you set a certain buffer size, and as you record, whenever that much sample data is ready to be written to the memory card, it gets written--drawing some extra current for a moment each time it occurs. You can see this if you're running on internal batteries, because there comes a point at which each write to the memory card causes the battery level indicator to dip momentarily.
If you record 16-bit, the buffer fills less rapidly than if you record 24-bit, so there are correspondingly fewer writes to the card per minute or per hour. As a result, somewhat less power will be consumed over, say, an hour's time at 16 bits rather than 24, and at lower sampling rates as compared with higher ones.
But whether that translates into consistently or significantly longer battery life, I truly don't know. I'm willing to change batteries more often than might be strictly necessary, just so that I don't have to worry about their running out during any part of a recording. As a result I couldn't even tell you approximately how long the unit will run on a set of batteries in any particular setting--long enough for either half of any classical concert I've ever recorded with it, is all I know for sure.
--best regards