Can Fluoride be absorbed into the blood from within the mouth without swallowing?
Although I'm having a hard time finding a source that provides specific information on fluoride in toothpaste, this review explains that fluoride is most readily absorbed through intestinal epithelia and that fluoride absorption through other tissues, such as oral epithelia, depends strongly on other chemical properties of fluoride-containing compounds: their 


  "reactivity and structure, solubility, and ability to release fluoride
  ions."


This suggests that you would need additional information concerning the overall toothpaste formula.

This review shows the rates at which fluoride ions are released from various toothpaste formulations. Figures 2 and 3 show that the highest discharge rate is roughly 1.7ppm and the lowest was just under 0.5ppm, both occurring after a 24hr period. The authors note in the discussion that these measurements are likely higher than what would occur in the mouth, since they had to use deionized water for their experiments, in which fluoride is more soluble than in saliva. 

Wikipedia lists fluoride toxicity levels as being between 0.5 and 1.0mg/L. Fluoride's molar mass is 18.9984 g/mol and this calculator shows that 0.5mg/L of fluoride translates to about 0.5ppm. While at first this makes the above results sound a dire, it's important to note that toothpaste remains on your teeth for far less than 24hrs and to remember that less fluoride is released into saliva than into deionized water. 

Wish I could find better results on how much fluoride might be released during a typical toothbrushing session, but I'm inferring from the linked review that it would be small enough to not merit a health concern. 

I emailed a dentist friend for more info and will update this post as I hear back from him. 

As for the comment about glands, it's important to understand that the glands found in the mouth are secretory glands, which means that they are optimized for discharging fluids and not for accepting them. 

--Update--

My dentist friend wrote back, confirming that no significant fluoride absorption occurs through the gums. From him: 


  the only significant absorption would be through swallowing fluoride.
  Any that was just in the mouth would not be well absorbed...
  that is why we do the high dose swish and spit treatments is to avoid
  fluorosis but deliver sufficient fluoride to the teeth.


In short, it looks like the answer to your question is: no, fluoride is not significantly absorbed into the blood from within the mouth without swallowing.