Yes, its ok. The radio will draw from the battery though, not the charger.
Also, the charger will not charge the battery if the radio is on. I left mine on all night in the cradle and the battery was completely dead in the morning. The little green light was on though saying that the battery should have been charged.
There might be a 2-3hr timing circuit in there that stops charging. I imagine that it hit that marker, turned the green light on, and then just let the battery die.
Strange.