How is the fluoride in toothpaste absorbed?
The chemical mechanism by which fluoride protects teeth is the remineralization of hydroxyapatite $\ce{Ca5(PO4)3(OH)}$ in the tooth enamel into fluorapatite $\ce{Ca5(PO4)3F}$:

$$\ce{Ca5(PO4)3(OH) \ (s) + F- \ (aq) -&gt; Ca5(PO4)3F \ (s) + OH- \ (aq)}$$

This reaction occurs at the surface of the enamel, i.e. directly within the mouth.  The fluoride ions participating in the reaction are dissolved in the saliva and other fluids present in the mouth.

Thus, the fluoride does not need to be absorbed into any part of the body (although, as part of the remineralization process, it can be said to be absorbed directly into the tooth enamel), and, in particular, there is no need for it to be swallowed.  Indeed, because of potential adverse effects of high levels of fluoride when absorbed into the body through the digestive tract, swallowing strongly fluoridated dental care products like toothpaste or mouthwash should be avoided.

That said, any fluoride that is swallowed and absorbed into the body, e.g. through fluoridated (or naturally fluoride-rich) drinking water, can still contribute to the remineralization of teeth, simply because some of it will be secreted back into the mouth as part of saliva.

While the fluoride levels in saliva (assuming a safe level of fluoride intake) are much lower than those in, say, toothpaste, your teeth will be constantly exposed to the fluoride in saliva, whereas they will only be exposed to toothpaste for a few minutes each day.  Thus, while the rate of remineralization due to systemic fluoride may be much slower than that due to e.g. fluoridated toothpaste, the total amount of remineralization per day may well be of a comparable magnitude.