This is probably true- but consider the case where the deadline is set at "never." Having frequent, small, imminent deadlines seems to be good practice, and is behind things like Beeminder.
No deadline, hmm... my reading list, for example. I'm working my way through it... I guess anchoring predicts that I'd work through it slower if I put deadlines on when to finish each book, since I'd anchor on the deadlines?
Whether or not I anchor on deadlines, though, I'd definitely read faster if I had imminent deadlines on each chapter, rather than a distant deadline for the whole book.
The phenomenon of anchoring seems to predict that deadlines will cause you to start a project near the deadline.
In more detail:
Any number you consider as an answer to a question will become an anchor and draw your answer towards it. Since you consider a deadline as a time to finish a project, your decision about when you should actually finish the project will be drawn towards it.
That'll make you start the project later, even though you know consciously that planning to finish a project near the deadline is a bad idea.
It's analogous to an example from Kahneman's Thinking, Fast and Slow—people buy more cans when there's a sign telling them that they can only buy 10.
So, what I'm predicting is that anything that prevents anchoring will reduce procrastination when there's a deadline. Consciously deciding when you plan to finish by adjusting from a much earlier time, maybe?
EDIT: Brendon_Wong points out that "procrastination" really refers to putting things off, which has an emotional cause. I think he's right. What I'm talking about isn't really a procrastination, then, but bad planning.