Yes, it's a great idea. Just look on wikipedia: country pages are very standarized, including the table with basic facts and the names of the sections.
The country tag wiki should include the most important about the country, from expat's point of view. It will surely be the population of the country, the percentage of immigrants, the official languages, and the languages spoken so broadly that knowing them would be a great help if you don't know any of the official languages (like Turkish in Germany).
Basic VISA informations, fist steps in given country (for US folks registering your address by local government isn't probably very intuitive). How to apply for job, how to apply for citizenship, banking issues (for example, you can pay money out from ATMs in Germany using VISA/MasterCard, but most shops accept only Germany payment cards).
There are for sure much much more but we don't have to give it all at once. Just move in that direction.
Please pick one country tag that will be the example to follow. Any edits to that tag will be carefully monitored by community, and format issues can be discussed on Meta. The editors of other wikis will have a great example to follow doing their edits.