[jaysdailydose]

Like RchW said, you can keep it out of the almanac.

But, each player will have their draft position and the like mentioned in their history files.

I get what you're trying to do... you just want new players to appear to fill in the rosters. One thing I can think of is just to manually fill the rosters after each offseason. The "Fill Teams with Fictional Players" option. This would just add players up to the roster limit each time you run it. Seems like it would accomplish what you want. (No mention of a draft whatsoever, and new players filling in the vacated roster spots.)

There would be mention of the draft in the news logs as well, but unsure if you'd be saving those, if that "workaround" doesn't do it for you.