If platonic principles exist (i.e., they have the ability to cause the universe, cause particular laws, etc), then I think this does imply some form of theism (not a patriarchal deity, however).
Here's why. If a logical principle 'exists' then this implies non-material ontological structure to the primordial world. Such a structure would encompass not just the principles, but all the principles and logic that could conceivably be a consequence from a particular principle. Let me illustrate. Let's say that A=B, then unless we are talking about a certain higher math, it would appear that B=A. What we have is one principle (A=B) directly implying yet another principle (B=A). In that sense, not only would all the laws and equations of mathematics *BE*, so would entire sets of algorithms: infinite algorithms.
The criteria of an algorithm existing is simple: it exists because it has to because it is a derivative form of another algorithm. What I think we have here is one eternal and infinite logical structure to the primordial world that collectively causes the world.
This is not a proof, but simply a conjecture. It seems to me that a theistic interpretation to nature is at least allowable. What is not allowable would be anthropomorphic descriptions (i.e., beyond metaphor). The full nature of that logical structure would be beyond our comprehension however.
Warm regards, Harv