You can do that but any pickup you put in the bridge position will sound like a bridge pickup. This is due to the fact that string movements are different near the bridge than they are near the neck.
If you use the neck mainly because that is your playing style then I would not worry too much about the bridge pickup. However, if you use the neck pickup also because you don't like the way your bridge pickup sounds then you should think long and hard about what exactly you don't like about your bridge pickup and what you want more/less of.
Cheers Stephan