Not so sure about time sheets or whatever, but I do know I'd strangle someone to get a proper database over a series of filing cabinets and paper records. Especially if the folks running and maintaining it aren't goddamn idiots and set up a solid and consistent system straight from the start, and bloody well leave it that way. It is a
metric fucktonne faster to hit ctrl+f <name> than dig through dozens/hundreds of files looking for said name. Several times now I've embarked on projects (helping with one of the local schools, sorta') whose time investment would have been cut to tenths or less if it had been digital. Mind you, it would have been cut to three quarters or a half if the filing system being used hadn't been shit (and had like five different people doing things differently involved >_<), but still.
Still, as some major conservationist dude whose name I've forgotten said, it's not the shovel, it's how you use it. Methodology will always be more important than technology, and no matter how good the latter is, if the former's buggered it's not going to help.
But, with proper methodology, technology is a force multiplier, so to speak. It's just that said proper methodology is somewhat staggeringly lacking in a lot of cases