Short answer: no, your dog is not "vaccinated".
I couldn't find any specific numbers about how many doses of adder venom are required to build up a tolerance, but from all I could find it takes a lot more than just 2 doses.
In the production of antitoxins the animals (usually horses) get administered small amounts of venom in increasing dosages. Just 2 injections are usually not enough to get the body to produce enough antigens or enzymes to consider the animal "immune" to a full dosage of venom.
However, adder bites seem to be not very lethal, unless you (or your dog) are allergic to the venom and get an anaphylactic shock. This allergic reaction can set in from 5 minutes up to several hours after the bite and must be treated immediately. You can read more about adder venom and its effect of humans, cats and dogs in this answer.
The study Persistent hypercoagulability in dogs envenomated by the European adder (Vipera berus berus) reads:
Envenomation by the European adder, Vipera berus berus (Vbb), is a medical emergency.
Hypercoagulability was measured in dogs up to 15 days after Vbb [Vipera
berus berus] envenomation. Dogs treated with antivenom may be less hypercoagulable than their non-antivenom treated counterparts. Thrombin generation is a promising diagnostic and monitoring tool for Vbb envenomation.
That means even if your dog doesn't show any symptoms of a snake bite, there's still an increased risk of it developing life-threatening thromboses for more than 2 weeks after the bite.