Yes rain can affect the properties of the concrete and all depends on intensity of rain and when it was started.
Concrete is homogeneous mixture and considered as impermeable, if the rain starts after placing and finishing of concrete, if intensity is less, it will affect the concrete by less proportion and mainly the top of the concrete gets affected.
There is no record on intensity of rain and alteration in properties of concrete which is freshly placed into structure.
Freshly placed concrete may have alteration in top layer due to increased water at surface as the rain wont make remixing of placed concrete, you can treat the top surface of structure by re-finishing it.
In case of column and walls where next flight above it to be casted, rain may be considered as good for it. it helps in making construction joint by removing lattice from top.