They’d have gone through the stomach first, which is basically an acid bath with added protein-digesting enzymes. Acid denatures proteins, destroying their bonds and structure – effectively causing them to ‘crumble’ apart. Wool, a protein, wouldn’t survive that in its thread-like form.
However, there is a condition in which people swallow large amounts of (usually) their own hair: trichophagia, sometimes called Rapunzel Syndrome. This can cause a large hairball to form, which can harden into a stone-like substance called a trichobezoar. Simply put, the quantity ingested has overwhelmed the stomach’s ability to digest the protein. Some people have become seriously ill as a result, and at least one is known to have died.
In short, a few strands of wool should not cause difficulties – just don’t eat anything bigger than an egg-cozy.