I have not noticed a big difference between adding the yeast at first or not. This is not such a big deal.
Yes it gives your dough a little extra fermentation time, but that's about it.
I think the difference may be material but I am not sure I can prove it, at least not yet. I also think it depends on the duration of the autolyse and whether the dough goes through another rest period before going into the refrigerator.
This is a subject that I have been thinking about quite a bit recently, especially after the exchange I had with member petesopizza at this thread: http://www.pizzamaking.com/forum/index.php/topic,3587.msg30225.html#msg30225
. petesopizza believes that adding the yeast later is better than adding it sooner, so long as the finished dough is given a few days of cold fermentation. Member giotto was also a proponent of the late addition of the yeast. In his case, and petesopizza’s case as well, the yeast in question was active dry yeast, not IDY. If the case for later addition of the yeast holds in the absence of an autolyse, I believe it should hold for the autolyse case also.
For purposes of this discussion, let us first assume that the yeast is added at the beginning of the autolyse. If the autolyse period is fairly long, say, around 20-30 minutes (which is typical), and was preceded by a reasonable amount of mixing, then it seems to me that the yeast, and especially instant dry yeast (IDY), will have been sufficiently activated by the liquid (water) and provided with sufficient oxygen (through the initial mixing) to start to reproduce (bud). With sufficient agitation and dispersion of the yeast, as occurs with the initial mixing in a fairly liquid environment, it will reproduce better. At some point, the process goes from aerobic to anaerobic (from oxygen to no oxygen) and fermentation starts and carbon dioxide and ethyl alcohol are produced by the fermentation. It does not take much to get the IDY activated because it is of relatively small particle size (smaller than ADY), it has more active cells (fewer dead cells than ADY), and is of a strain and shape that is conducive to faster action so long as it is not shocked by cold water (as Jack has noted). Once serious kneading begins, the IDY will continue to ferment the sugars in the dough and, as the heat of machine friction increases, the fermentation process will accelerate accordingly.
Now, consider the case where the IDY is added at the end of the autolyse. In this scenario, and all else being equal, the IDY will still activate once it is added to the dough because of the presence of the water, as before, but if there isn't enough oxygen in the dough at this time to promote healthy reproduction of the yeast, the yeast may instead use the sugars in the dough to produce carbon dioxide and ethyl alcohol rather than for reproduction purposes. From what I have read, it takes about twenty minutes for the yeast to bud (reproduce). If the duration of the knead is less than twenty minutes, which it seems it should be because of the effects of the autolyse to reduce total mix time, then the yeast energy levels should be reduced and the rate and extent of fermentation should be pegged at lower levels than for the first example. Also, the finished dough should be subjected to less machine frictional heat because of the shorter mix time. Moreover, if the dough goes into the refrigerator immediately, rather than after a second rest period, the rate and extent of fermentation will be further reduced. The difference in the useful lives of the two doughs in my two examples may be far more than the duration of the autolyse period(s). Maybe it is possible that adding the yeast to the dough at the end rather than the beginning will buy a couple of days more of useful life.
If my assumptions and analysis are correct and a materially longer fermentation time is desired, then it may be better to add the yeast toward the end of the process rather than at the beginning.