Yes, but to a way lesser degree.

The bombs become really nasty by creating a big chain reaction (boom) and then radiating the dust the explosion creates (aftermath) which then spreads everywhere.

Without a controlled explosion there will be significantly less radiating reactions and radioactive dust.

It's like deep inhaling the smoke of a package of burning fire starters VS throwing said burning fire starter into a warehouse full of fireworks (and for the sake of this argument you cant leave the warehouse and have no equipment whatsoever)

Both will probably fuck you up a bit if you're to close, but one is comparably insignificant.