Consecutive giving is one of my favorite ways of recognizing donors, because it promotes loyalty.
I’m not sure the question is the right one to ask: does promoting loyalty increase donor participation? Well, it increases the number of loyal donors which should free up some resources to invest in recovering or acquiring other donors.
I.e. if you are growing a 3+ year loyalty society, then presumably you have more donors with a high retention rate (retention rates grow with each year of consecutive year and tend to level off around 3-5 years consecutive), which means that you don’t have to spend so much to keep those donors, so you have more money for giving days, crowdfunding, etc.
But honestly, the biggest benefit of increased loyalty is that consecutive donors are much more likely to make major/planned gifts.