Not in the campaigns, no.  In fact, I'm fairly positive (although not entirely certain) that this is true for all campaign missions.  In Sandbox, yes.  In the various scenarios/custom maps available, it varies.

Scenarios, maybe.  I think some of them may have anomalies disabled, actually, which would make them useless.  Been a while since I looked, though.  In the campaign, they're practically worthless.  I can't remember a single instance of needing or wanting them, although you may desire some form of scoutship.

Anomalies really don't make that much difference in most games (whether it be generic sandbox, scenario, or campaign); they're mostly there for flavor.  They can certainly provide an early boost in a colonization-heavy game, particularly if you get your fair share of 500bc/1000bc anomalies, but for most games you might not even notice if they were gone.  Though I suppose they do make a fair bit more difference in all-rare setups, or tiny galaxies, where there's not much else to go around.

That said, they're one of my favorite little things about the game, and I was really happy when they started respawning as of DA 1.8 or so.