No.
Just because a program compiles and runs does not mean that it is correct. For example, say that your assignment is to create a program that will write "Hello World!" on the computer monitor. Here is the program you have created:
class Hello
{
public static void main ( String[] args )
{
System.out.println("Hello Neptune!");
}
}
When a program compiles without any syntax errors, but does not perform as expected when it runs, the program is said to have a bug.