EDIT 2: just thought of another question. Mines improve the output no matter what, but will the mines automatically discover copper or iron and so forth when I get the tech for the resource? Is there a smaller chance of discovery of resources if I make a mine before I get the tech for it, than if I wait until the tech is researched?
I think you misunderstand something here, so I just want to clear it up.
There's two ways of getting hold of a mining resource (metals and gems and so on).
The first way is to discover the technology (for instance, Bronze Working) that
reveals the resource (for instance, copper). Note the emphasis on "reveals" - the game doesn't create the copper resource when you discover BW. The locations of resources are set from the start of the game; you just can't see all of them. So if you build a mine on a hill
that just so happens to have a hidden copper on it, then once you discover BW you will automatically have that copper.
The second way is the one that involves chance, and this is the one Roland was talking about. When your city works a mine tile that has no resource (visible or not) already on it, there's a tiny chance every turn that a mining resource (of a type you can already see) will be created there. When you mouse over the icon for "build mine" and it says "chance to discover gold, silver, gems" - this is what it's talking about.
So in short, you could say that technically, building a mine (
and working it) before you have BW will lessen the chance that you "discover" (as in the second way) copper, since there's a chance that you will discover some other resource there and therefore never be able to discover copper there - but it's such a miniscule thing that you shouldn't even be considering it.