I am using DESeq2 to estimate fold changes between two conditions neither of which have any replicates.

Will it be of any utility to use log2fold shrunken changes over the non-shrunken ones in this case?

For no replicate experiments, I'd suggest applying the vst() and then you can just calculate the simple difference between the two samples. This will give you a log2 fold change that is moderated, such that small counts do not produce large LFC (avoiding having to pick a pseudocount).