Many people have asserted this, but it's not true. As long as ReSharper is active it does have a performance impact. The impact varies depending on the current action, and yes opening a new project does have the largest impact.
Honestly, I'm done giving ReSharper chances. Of all the times I've tried it, I've yet to encounter any feature that justifies the wet blanket thrown over the IDE. I've tried on large projects and small projects, across multiple computers. I've followed JetBrains' recommendations for improving performance. The performance impact is noticeable, and the UX drives me nuts.
Like I said, I like some other products from JetBrains, but ReSharper just isn't for me. If it works for you, and the impact is negligible enough to not matter, thats great.