Yes. But it only counts full sets of outfit styles your character has learned. It's not enough to learn just a few motifs here and there. You need to complete the sets.
From my testing, the base rate for a master writ from Blacksmithing, Clothing, or Woodworking (the 3 to be affected by motif knowledge) is about 5% at base level, and can go upwards of about 20% when you know all the traits and all the motifs (that's about the rate my main gets).
Learning the traits appears to be a 3-4% increase in the drop rate... and the motif knowledge appears to be "front-loaded", so that you get a larger increase in drop rate from the first full purple motif you learn than you would from the 50th
I have alts who know between 50-75 motifs (not all ~100 like my main) and their drop rates are not much lower than those of my main (within 1-2%), but my alts who only know 3 or 4 motifs (the ultra-cheap ones), tend to have drop rates more in the 8-10% range (they do know all the traits)