Does it violate the standard for a non-default-constuctible struct to lack a user-defined constructor?

It is possible to define a struct (a) that has no user-defined constructors, and (b) for which a default constructor cannot be generated. For example, Foo in the below:

struct Baz
{
   Baz(int) {}
};

struct Foo
{
   int bar;
   Baz baz;
};

You can still create instances of Foo using aggregate initialization:

Foo foo = { 0, Baz(0) };

My normal compiler (VS2012) will grudgingly accept this, but it raises 2 warnings:

warning C4510: 'Foo': default constructor could not be generated.

warning C4610: struct 'Foo' can never be instantiated - user defined constructor required

Of course, I've just proved warning #2 wrong--you can still instantiate it using aggregate initialization. The online compilers I've tried are happy enough to accept the above, so I'm guessing VS2012 is just being overly-aggressive with this warning. But I'd like to be sure--is this code ok, or does it technically violate some obscure part of the standard?