Is it possble that a toothache cause trigeminal neuralgia?

Yes: A toothache can mimic the pain of trigeminal neuralgia, but depending on where the infection is located and how much it has spread, it could cause an inflammatory reaction around branches of the trigeminal nerve and cause trigeminal neuralgia. I wouldn't say that it's a typical cause for trigeminal neuralgia though.

Probably not: Trigeminal neuralgia is caused by a compression of the trigeminal nerve by the tissues of the face. This compression leads to intractable pain in the face. The treatment is to surgically release the trigeminal nerve from the impeding tissue. A toothache is caused by an inflammation of the nerve of the tooth or an abscess caused by the death of the nerve. This pain is eliminated by a root canal.

Yes: If toothache is associate with an infection in the bone it could very cause trigeminal neuralgia.

The opposite is true: "There is one disease of the Jaws which seems in reality to have no connection with the Teeth, but of which the Teeth are generally suspected to be the cause. As simple pain demonstrates nothing, a Tooth is often suspected, is perhaps drawn out; but still the pain continues, with this difference however, that it now seems to be in the root of the next Tooth". John Hunter (1778). It is true today.