Can addition of two band limited signals create aliasing?
Ideally no, adding 2 signals should result as a simple sum.

provided you don’t clip

DSP systems have finite dynamic range. A double float has a very large dynamic range so it is not usually a consideration.  

Fixed point arithmetic has uniform quantization but the finite dynamic range requires attention. 

Floating point is not a uniform quantization, so arithmetic also introduce rounding, which are discontinuous on small scales.