To the extent that there's a lot of slack in the economy, factories laying idle and so forth, more money will tend to result in more production rather than more inflation. Now there are always some sectors of the economy that aren't idle so more money will always result in at least a little inflation, but in the case of the Great Depression this was very little. And they were experiencing deflation at the time anyways, so more inflation would have gotten them closer to price stability.

Giving money to the needy has different effects than that.

For one thing, if you finance the handouts with taxes rather than printing money, they will have no effect on inflation.