Irish moss or whirlfloc doesn't coagulate protein, it helps drop it out of suspension after the boil. This allows the break material to be left behind in the kettle. What better time is there to take advantage of this?
I'm not going to get in a silly argument here, but Irish moss/Whirlfloc works to help to coagulate proteins because of the electrical charges of particles, just like other clarifers like chitosan. IM is negatively charged. Once it coagulates, the heaviness of it causes it to drop out. Whether you strain it or not, it's coagulated.
"During the wort boil, certain types of proteins can be coagulated. These proteins are primarily responsible for haze formation in the finished beer. However, the boiling temperature alone will not coagulate the proteins. Coagulation and precipitation require the action of the bubbles formed during a vigorous boil. Because these proteins are electrically charged molecules, providing a substance of the opposite charge will enhance the coagulation. Irish Moss, carragheen, is a seaweed that when added when added at the rate of 1 teaspoon to a 5 gallon batch the last 15-20 minutes of a rolling boil helps attract coagulated proteins into clumps causing their precipitation during the cool down period.
The importance of a vigorous, rolling boil for protein coagulation cannot be emphasized enough." Alberta Rager
and
Many brewers, both professional and amateur, use kettle coagulants such as Irish moss (red marine algae Chondrus crispus and Gigartina stellata) and its derivatives to increase trub coagulation. The Irish moss, a negatively charged colloidal material, attracts positively charged proteins in the wort to form larger hot trub particles. In its raw form, 4-8 g/hL (4.7-9.4 g/bbl) Irish moss should be added to the boiling wort appromimately 15 min before knockout. Because treatment with Irish moss can cause the wort to foam and boil over, watch the boil and be prepared to reduce the heat going to the kettle. Irish moss is more effective if first diluted in water and let to stand for at least a couple of hours (preferably overnight), thus promoting swelling and gelling action (1). Incidentally, for those Reinheitsgebot purists, the addition of kettle coagulants is not allowed. Ron Barchett, Brewing Techiques
and from BYO:
Kettle finings are coagulating agents added to hot wort, typically toward the end of boil, to aid in the precipitation of cold break. They are also referred to in the industry as copper finings because they are typically utilized in the kettle: often called the copper in the UK.
There are several types of finings. One is Irish moss, a red seaweed or algae that is rich in carrageenan. Irish moss contains polysaccharides that carry a negative charge that readily binds with positively charged proteins in the wort. This binding activity results in precipitation of these proteins after the wort is cooled. These finings are utilized predominantly in the ale brewing world and are not as common in the lager world. They are considered a process aid and are not technically an ingredient since it precipitates out of solution or is filtered out of finished beer.
We utilize kettle finings to aid in producing clear (cooled) wort and ultimately clearer finished beers. Utilizing kettle finings results in beer that is much easier to filter, or if you dont filter, beer that naturally drops much cleaner.
Kettle finings also improve the physical stability of beer by removing haze potential proteins. These proteins, if left in the beer, will eventually combine with tannins and form haze. In other words, the removal of potential haze-forming proteins results in a beer that is not only less hazy when finished or filtered, but stays bright for a longer period of time after it is packaged.
These finings are excellent at binding with these proteins and work to remove them from solution through precipitation. The resulting complex tends to settle out and is removed with the yeast at the end of fermentation.
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The proteins precipitate out, regardless of the exact cause. But, you can definitely see them coagulate and "glob up" in a batch with whirlfloc vs. no finings. I can make clear beer without kettle finings, but whirlfloc makes it easier.