As a native speaker: Generally no, but it depends.
The "t" in "Rat" is pronounced much harder than the "d" in "Rad" is. BUT: The more and more you go into the north of Germany, lets say Hamburg for example, they have a very similar pronouncing of "t" and "d". Both often sound very hard (more like an "t"). Whereas people in the south tend to pronounce both letters more soft, like a "d".
But in general they are pronounced differently.
The "t" in "Rat" is pronounced much harder than the "d" in "Rad" is. BUT: The more and more you go into the north of Germany, lets say Hamburg for example, they have a very similar pronouncing of "t" and "d". Both often sound very hard (more like an "t"). Whereas people in the south tend to pronounce both letters more soft, like a "d".
But in general they are pronounced differently.