Can the Number class be used as an argument to accept numbers of all types as parameters?

Yes, autoboxing works to convert int to Number just as well as from int to Integer:

public class Test {
    public static void main(String[] args) throws Exception {
        foo(10);
        foo(10.5);
        foo(10.5f);
        foo(java.math.BigInteger.ONE);
    }

    static void foo(Number number) {
        System.out.println(number + " " + number.getClass());
    }    
}

Or rather, boxing itself only converts from int to Integer, but then a widening reference conversion converts from Integer to Number. From JLS 5.3:

Invocation contexts allow an argument value in a method or constructor invocation (§8.8.7.1, §15.9, §15.12) to be assigned to a corresponding formal parameter.

Strict invocation contexts allow the use of one of the following:

• an identity conversion (§5.1.1)
• a widening primitive conversion (§5.1.2)
• a widening reference conversion (§5.1.5)

Loose invocation contexts allow a more permissive set of conversions, because they are only used for a particular invocation if no applicable declaration can be found using strict invocation contexts. Loose invocation contexts allow the use of one of the following:

• an identity conversion (§5.1.1)
• a widening primitive conversion (§5.1.2)
• a widening reference conversion (§5.1.5)
• a boxing conversion (§5.1.7) optionally followed by widening reference conversion
• an unboxing conversion (§5.1.8) optionally followed by a widening primitive conversion

In this case the loose invocation context is used (for the first three invocations of foo) as no method declaration can be found using strict invocation contexts.