Can "Be under no illusion" have both positive and negative connotations?

I agree with you that this, at best, is an unusual use of the phrase "be under no illusion", while not saying that it's necessarily wrong.

The phrase implies that someone might develop, or has already developed, an illusion (a distorted view) of something. So perhaps if the conventional wisdom was "2011 is not going to be our year", the phrase "Be under no illusion, 2011 is our year" might make more sense?

As a native (US) speaker, I find the phrase odd-sounding. I don't believe I've ever encountered it. Despite that, I wouldn't interpret that phrase as inherently positive or negative; the clause that follows would determine that. However, I would interpret 'don't be fooled' the same way. In each case, the speaker is trying to disabuse someone of a concept that the speaker finds incorrect in and of itself, whether or not that incorrectness is positive or negative.

Edit:

I encountered a billboard the evening after I posted this answer, with the more common phrase which I could not remember at the time: "Make no mistake". Applied to the original statement, it would be "Make no mistake - 2011 is Our Year."

Interesting question, xiao: running over the possible implications of the phrase, I think it contains both positive and negative allusions.

Thus, "don't be fooled ...it's going to be tough" is a legitimate reading, and the one that I'd have arrived at first.

Equally, it can be seen as "don't be fooled [by the naysayers] ...we'll perform superbly."

Personally, I sense a subtle threat in the phrase no matter how it's read: the subtext says "don't be an idiot; believe what we're about to tell you, or else ...".