Is bounded-width SAT decidable in logspace?
Indeed, using the resultss in Elberfeld-Jakoby-Tantau-2010 one can 
show that SAT can be decided in logspace on formulas whose incidence graph has bounded treewidth. Here is a sketch of how the main steps of the proof of this claim go.


The notions of tree-decomposition and treewidth can be generalized to arbitrary relational structures. See for instance sections 2 and 3 of 
this paper by Dalmau, Kolaitis and Vardi.
Courcelle's theorem states that MSO logic can be decided in linear time on relational structures of constant treewidth. 
A theorem of Bodlaender implies that if a relational structure has treewidth $t$, then a tree-decomposition of such structure can be found in time $f(t)\cdot n$. In other words, such a decomposition can be found in linear time on graphs of constant treewidth.
One can define suitable relational structure $\tau$ which can be used to encode a formula $F$ together with its incidence graph $I$. The treewidth of $\tau$ is at most a constant plus the treewidth of $I$. 
The set of relational structures $\tau$ which encode satisfiable formulas + their incidence graphs is MSO definable. 
Therefore, by Bodlander+Courcelle's theorem, one can decide whether a formula of constant treewidth is satisfiable in linear time. 
Elberfeld-Jakoby-Tantau-2010 show that "linear time" can be replaced by "logarithmic space" on both Bodlaender and Courcelle's theorem. 
Therefore, for each MSO formula $\varphi$, and each relational structure $\tau$, one can determine in logarithmic space whether $\tau$ satisfied $\varphi$. 
In particular, SAT can be determined in logspace on graphs of constant treewidth.