Noting that the rules state that a grappled ship can’t evade, there is no mention of a ship at anchor. Has implications for a failed tacking attempt as well as for ships already at anchor.
I don’t have time right now to read closer, but I assume that the general rule is that all ships get to roll for evade, unless the rules specifically mention some exceptions.
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As Fred says you always get to roll for evading unless grappled.
If you think about it like this, even at anchor the crew are frantically working to get the ship out of the way, but when grappled they are locked to another ship and no amount of wheel turning or sail trimming will change their position.
Also, welcome to the forum 
The Evading Rules as written does not make exception for Anchored ships, whereas they do for Grappled ships, which implies that not only Anchored ships can avoid collisions, but also they were meant to. More so although Grappled ships become Anchored as a result, these are two completely different states and two different Keywords.
Additionally an Anchored ship can still make a turn during activation. I see no reason why wouldn’t it be allowed to Avoid collisions.