I have used our compost to amend the soil when planting blueberries, successfully. But I don't have any blueberries growing next to the pile. In general, blueberries do best with full sun, all day. They can be grown in full sun, half day, but they will not produce as much fruit. They have to have some moisture around the roots, but they will not do well if the ground is continually saturated. If I had to choose between blueberry shrubs and raspberry canes, next to the compost pile, I would plant the blueberries, because they are more easily pruned and kept in check. Raspberries tend to spread agressively.

I wonder if they would be ok with the nutrient balance around it. I've read that they're sensitive to fertilizer, but compost probably wouldn't be as strong, so it might be ok... Just something to think about I guess.

Have you tested the acidity around the bin?

Not tested for acidity, but assumed. Only thing that does well is forsythia, but they don't produce fruit :)