Having grown Rye for some time as a seed crop (vs only as a cover or forage crop), I have observed some interesting things on our soil type (light sandy loam). 

NOTE:  We have NEVER applied any herbicide to the standing Rye crop.  In some occasions we have burned down the field after harvest if tillage is not doing a satisfactory job of weed control.

The competition effect seems to be two fold.  Both aggressive early growth to help choke out competing weeds as well as a chemical effect that "retards" the growth of weeds.  In this regard Rye really does not "Kill" weeds but merly suppresses the growth.  I make this comment on the observation that there is usually not much weed pressure on the ground until after the crop is harvested.  Once the crop is off, the weeds start aggressively growing within one or two weeks depending on the weather. 

The abnormal weather over last spring and summer brought to light some interesting aspects of how this might be working.  We had a warm yet dry spring and since we did not have a good spring rain to warm the soil and take out the frost in an even fashion, the Rye crop did not grow as quickly and aggressively in the spring.  I would have thought that the cool wet summer that followed would have been conducive to this cool season crop but instead it seemed to suppress its growth substantially (harvest was over 3 weeks late).  This allowed for weeds to increase their pressure on the crop.  I am guessing that although the Rye was establishing a cover and emitting the alleopathic chemicals, the weeds that were a little more mature than normal by this point were less effected. 

Long story short, last year the Rye crop did not do as good a job competing against weeds.  I think if it was purely a chemical effect that the Rye would have been able to do better.  The key then seems to be both its ability to grow quicker in cool soil early in the spring thus having a better impact on the younger weeds from both competition as well as any chemicals it may emit.

This was strikingly apparent in two side by side fields.  One had Rye on Rye for several years in a row, thus creating a fair weed seed bank that in normal years could be controlled by the Rye with no added chemicals.  The adjoining field had a crop history of Sunflowers followed by Spring Wheat last year.  Thus, this field had a fairly aggressive chemical weed control program for a few years before.  The field following this cleaner wheat field did substantially better yield wise, quality wise and with a more consistent maturity (this year many fields had a very high degree of uneven maturity).  This field is the source of the Rye crop I still have in my bin that has high enough quality for milling.  The others all had to go for whiskey which has lower falling number standards.  Many nearby growers has such a severe level of sprouting it would not even make whiskey.  Although sprouting is not a direct result of weed pressure, the weedier crops had more touble drying down and a slower, more uneven maturity.

As a side note: Historically, on a few fields that we had a history of very high levels of quack grass pressure, the Rye on Rye for 3-4 years with tillage practices that involved a digger did an excellent job of almost removing the weed completely.  I assume this is due to quack grass mainly reproducing via rhizomes.  Other weeds such as ragweed, lambs quarter and foxtail that seem to be able to grow and produce seeds quickly between harvest and fall tillage seem to continue to maintain a bank of seeds in the seedbed area. 

With Rye, I have never "personally" observed a lasting alleopathic that would effect the next years crop.  The potatoe growers extensive use of Rye as a cover speaks to this fact as well. This may be due to our well drained soils, harsh winters, or simply because the chemical it emits does not last long and breaks down etc.   I would hypothesize that if used as a fall/winter cover, an early and complete kill of the Rye as soon as possible in the spring would help lesson any alleopathic effect the crop would have.

Personally all the effect does for us is elminate the need to spray on the standing crop.  Rye does not really work well alone as a weed control as we have to augment our practices with timely tillage activities and/or a burndown application once weeds sprout but before they can go to seed.

Thats my limited knowledge on the topic.  Hopefully my observations might help on the subject.