Is make_unique in initializer list in copy constructor good purpose to not use noexcept specifier?

The cpp coding guidelines are pretty clear about it in E.12: Use noexcept when exiting a function because of a throw is impossible or unacceptable

So you can use noexcept even if the call of that function/ctor could result in an exception, if that exception would - in your opinion - result in a not handleable state of your application.

Example from the guidelines:

vector<double> munge(const vector<double>& v) noexcept
{
    vector<double> v2(v.size());
    // ... do something ...
}

The noexcept here states that I am not willing or able to handle the situation where I cannot construct the local vector. That is, I consider memory exhaustion a serious design error (on par with hardware failures) so that I'm willing to crash the program if it happens.

So if a failed construction of Foo can be handled using a try-catch block without serious problems. Then you won't use a noexcept there.

Reflecting on some other answers: I wouldn't use noexcept if a function potentially throws, even if you don't care if your program will terminate if it eventually does. Because it will, if a function declared as noexcept throws. Declaring your function noexcept holds semantic information for the users of your class, they can depend on this information, which is essentially untrue in your case.

EDIT: I recommend you to read Item 14 of Scott Meyers' Effective Modern C++, it describes well the benefits of using noexcept and when to use it.