I am doing some tests (naturally). I have applied fall fertilizer at intervals about 2 weeks apart in the fall on my neighbor's vacant lot, (non-irrigated, low maintenance). So far, if I look close, there is a stripe of slightly greener grass from the September 23rd treatment. Unfortunately the lot is not uniform, patches of shade and crabgrass--so--small differences would not show up.
Last year I did similar experiments on the lot, and my daughter's backyard. The differences were so slight, I could draw no conclusions.
On my own backyard, I did a similar experiment, with one 20 foot square area having double fertilizer on November first.
Shady yard, high quality bluegrass--by November 30 there was no visible difference. There was no visible difference during the following year.