I had a noticeable drop, I'd say, within 4 - 6 weeks, but possibly sooner.
I basically cut most carbs on Dec. 1, when I got the scary phone call. Then, within a couple weeks, I had read this forum and pretty much dropped the few remaining "hard-core" carbs (pita, quinoa) so all I get is whatever is in the non-starchy foods I eat: veggies, milk in my tea, occasionally a few red or black beans, incidental sugars in sauces at restaurants.
I started testing daily on December 20. My FBGs then were somewhere in the 120s and low 130s, with an occasional reading in the 140s.
By January 5 an 6, my FBGs were in the low 100s. Then they slipped occasionally into the 90s. That seems to be where they are right now and have been relatively stable for a little while - they're falling between 90 and 105ish. (Some fluctuations back up late January - possibly due to hormone fluctuations. I'm watching that.) But the A1c results seem to indicate that despite the mornings being higher, the rest of the day isn't peaking high. There might be some morning dawn phenomenon going on there.