What does vitamin B6 and B12 absorption depend upon?
Vitamin B12 (cobalamin) is a water-soluble vitamin required for homocysteine methyltransferase. In order to be absorbed, it must bind to intrinsic factor (IF), which is produced by the parietal cells of the stomach. The absorption of the vitamin B12-IF complex occurs in the terminal ileum (of the small intestine). The quote just means that if there isn't enough IF, then you can't absorb vitamin B12.

There are many things that limit absorption of vitamins, and even vitamin B12. Because vitamin B12 is found in animal products, vegetarians and vegans may need to supplement it. Pernicious anemia is an autoimmune disease that destroys IF or the parietal cells, Gastric bypass surgery can lead to vitamin B12 deficiency. Anything that affects vitamin B12 absorption in the terminal ileum, such as in Crohn's, celiac disease, or enteritis, can lead to deficiency.

To answer your question, no. Yes, it will use some IF (provided you have IF), but that would allow your body to absorb vitamin B12. For people who have diseases mentioned above, they can take vitamin B12 via injections, subligually (under the tongue), or intranasal gels, according to the fact sheet you cited.

Because all the B vitamins and vitamin C are water-soluble, they are easily absorbed through the intestinal wall. Excess amounts are usually excreted in urine. I believe vitamin B12 is the only vitamin that needs to be bound to a factor, due to its larger size. It can be stored in the liver for several years. Fat-soluble vitamins (A, D, E, K) are absorbed with lipids.