For a strongly convex function, does the initialisation of $x_0$ matter?

Question

So I am curious what the convergence conditions are for a strongly convex function using the Newton Raphson method. If the function is strongly convex then if the First Order Necessary Conditions hold, then surely we must always be taking steps such that $f_{k+1} < f_k$. This would lead to convergence for an appropriate step size.