Yes, and yes.
The hardest part of any project is the idea, so you've cracked that bit already!
Driving an LCD board generally requires a few GPIO pins, and there are alternatives, such as an I2C piggyback board, or even a serial board. However, if you aren't using the GPIO for anything else, why spend the extra money?
A 16x2 LCD is relatively straightforward. You need to work out the wiring for it, but conveniently, there is an article on the page you've linked to which explains how (although it uses a Pi Cobbler as well). If you're handy with a soldering iron and a spot-face cutter for strip-board, there are other ways to do it.
Don't be put off by apparent failures, and break down the project into small steps, which is my basic advice to anyone. The article on Adafruit shows how to do most of what you want, but working out what the uptime is isn't included - that's something for you to do.
Also, a more advanced version might be to 'scroll' the display, but don't worry about that to begin with.
No, I can't think of anything funny that won't offend someone if they want it to...