It's not likely. Usually when you blow fuses during an installation, it's because you've allowed a power wire to come into contact with dash metal or a grounded wire. (It happens a lot when people cut two wires at the same time; you get a short circuit through the wire cutters).
The result is a surge of current through the power wire, which blows the fuse. However, in a case like that, the surge doesn't get to the CD player itself, because the short is between the battery and the player. So the CD player shouldn't be affected.
That doesn't mean it's not possible to damage your new radio through faulty installation. However, in most cases, the radio will be unharmed by a problem that blows a vehicle fuse.
