Can the YangMills or ChernSimons action functionals be considered as [possibly perfect] Morse functions? I assume we would be in an equivariant scenario due to considering the configuration spaces with gaugegroups/transformations. Or at least how far away are they from a MorseBott function (and from being perfect)?
The problem with the CS functional is that the Morse indices of its critical points are infinite. In particular, this functional cannot be perfect. The Floer complex does not compute the homology of any particular space (though it might compute the homology of a certain spectrum). On 4manifolds the YM functional has some analytic deficiencies: it lacks PalaisSmale condition. This lack of PalaisSmale manifests itself in the form of "bubbling" which is a nagging issue to be taken seriously when defining Donaldson invariants. On 2manifolds it was investigated thoroughly by AtiyahBott. In that paper they describe how equivariant cohomology can be used to establish some forms of perfectness. 


Let's consider CS functional for concreteness. The problem is that CS is neither Morse nor MorseBott (because its critical points are flat connections and character varieties of 3manifold groups could be rather bad). The trick is to perturb CS to a Morse function. This was done first by Taubes ("Casson's invariant and gauge theory") and then developed into Floer theory. How far is CS from being MorseBott? If you consider $SU(2)$ connections then for Seifert manifolds the character variety can have quadratic singularities, so it's not a manifold. There are examples of hyperbolic manifolds so that the $SU(2)$ character variety has cubic singularities. In fact, for $SO(3)$ flat connections over 3manifolds the situation is much worse and you can have any singularity over ${\mathbb Z}$. I suspect the same happens even in $SU(2)$ case but it's harder to prove. So, perturbation to a Morse function is the only way to go. 


There's a generalization of MorseBott called MorseBottKirwan that you can read about in Kirwan's book. Basically this condition guarantees that the unstable sets are manifolds, but not the stable sets, so the negative of a function that's MorseBottKirwan may not be. If one defines a "YangMills functional" very generally to be the normsquare of a moment map, Kirwan proves that for $M$ finitedimensional, this normsquare is a perfect MorseBottKirwan function. (Of course the original example of such is on $M$ a space of connections, where AtiyahBott did the same, as I recall.) 


Here is a nontechnical answer to your question, which I bring up only to illustrate that your question is deep and wellstudied. A good cartoon picture of the homology groups Floer assigned to 3manifolds is that they are the "Morse homology" of Chern–Simons as a "function" (really, closed 1form with integer periods) on the stack of principal bundles with connection over the manifold. Choosing a metric on the manifold picks out a metric on this stack, and for that metric the gradient flows are the antiselfdual pure Yang–Mills instantons on the infinite cylinder over the manifold. This is, I think, well explained in Atiyah's paper 1988 paper "New invariants of 3 and 4dimensional manifolds", given at the Hermann Weyl centennial conference. 


This got too long for a comment. Atiyah and Bott showed that the YangMills functional on a Riemann surface is equivariantly perfect, i.e. it's perfect for gaugeequivariant (integral) cohomology. To be a little more precise, they showed that a certain stratification (the HarderNarasimhan stratification) of the space of connections is perfect in this sense, and Daskalopoulos showed (using Uhlenbeck compactness among other things) that this stratification does in fact agree with stable manifolds of the YangMills functional. (AtiyahBott had conjectured this, but did not prove it in their paper. Note that Uhlenbeck's compactness theorem came just after AtiyahBott.) For nonorientable surfaces, the situation is different: in some cases the YM functional is "antiperfect" in a certain sense, and in some cases it's neither perfect nor antiperfect. These ideas are discussed in recent work of Melissa Liu and NanKuo Ho, and also in recent work of Tom Baird. 

