Can the DFT can be performed without normalization?
Yes.  In fact, depending on your receiver architecture, you may not need the divide by $N$ in the receiver.
Generally, in a receiver you care about the relative phases of the bins (or possibly their strengths with respect to some other part of the same signal).  So there's no reason to do that multiply if you don't want to.
If you're working with fixed-point math, just make sure that you don't experience over- or under-flow.