"My ice cream arrived and it had melted."

I'm thinking, "My ice cream arrived already melted", is the idea you're trying to convey.

Yes, it's fine.

I suggest using past perfect to make it clear that the ice cream began melting before it was in your hand. "My ice cream arrived but it but had melted." "Was melted" is understandable, but it can mean a) the status of the ice cream was "melted" (which is what you mean) or b) when the ice cream arrived, somebody pointed a flamethrower at it.

Thank you Frank :)