It seems to me Frege understood the need in mathematics to talk about many different kinds of thing - numbers, truth-values, functions, and so forth - and to distinguish which kind of thing you are talking about; but not the necessity to use types (or other methods) to avoid circularity. Indeed, it is precisely the mistake Frege made in his attempt to axiomatise logic and mathematics and which led to Russell's paradox, that motivated Russell (and Whitehead)'s theories of types.

Frege certainly articulated a clear notion of what a function is, which is significant.