Log2 fold change correlation for ChIP seq data - do I need a FDR cut off?

Question

[brisbio]

I have ChIP-seq differential binding data for two transcription factors and a histone modification. I want to see if the change in TF binding/histone modification between timepoints are correlated with each other. Therefore I am going to correlate the log2 fold change for each factor. However do I need to apply a FDR (q-value) cut-off prior to my correlation (<0.05)? My thinking is the changes in TF binding between timepoints aren't 'real' unless they are significantly different.

[Rashedul Islam]

Why not applying thresholds for both fold-change and FDR?