Does it actually affect your prestige to have players drafted?

Yes

yes, slightly per player

Does the order of the pick affect it? IE first overall being more important than a second round pick? If I have 2 players drafted should I expect a bump up, or is it very slight?

The 1st pick in the 1st round carries the most weight and so on down the line. Having multiple players drafted is usually better than having 1 drafted. Your prestige is actually a decimal number and there are certain ranges for the grade shown. Different actions that you accomplish such as having players drafted also are represented as decimal numbers. If adding the additional number pushes you over a breakpoint, you will see a bump in your prestige grade. If it isn't enough to push you over the breakpoint you will not see a bump in your prestige grade.