This is easy enough to test with a few lines of code, but I think the answer is "yes" for both cases. Base-64 only uses non-control characters that are part of US-ASCII - those should have the same encoded values in just about any encoding.
As a rule of thumb, you shouldn't use new String(byte[]) and String.getBytes() without specifying the encoding; that's just asking for trouble.
Ulf: Thank you for your reply.
I tested the equality of(==) encoded characters in byteArray and characters in the array returned by String.getBytes(). Both were equal.
I also tested this by writing image data in Byte array, encoding it and then use the String constructor, getting the bytes and again reconstructing the image back. The image was same with no distortion(difference).
So, I think it is safe to assume that encoding is not hurt, atleast in this case.
Also, thanks for your advice about String constructor usage.
Cheers!