Pontious,
Article 5 is rather more detailed than that and doesn't mention the word "war" at all. Rather it uses the word "attack", which your incursion clearly would be. In such a case, the Article states that member states can then excercise the right to individual and collective self defence, taking such actions that are deemed necessary. Whilst those actions can include the use of military force, it doesn't mean everyone goes to war.
So, in the case of your mystery attack by an unseen enemy, the state that was attacked could invoke Article 4 on the grounds that its security had been threatened. Thereafter, it would be for member nations to decide what action should or could be taken. That may be anything from a stiffly worded rebuke to offering security assistance to armed deployments. Every situation is different and it is for NATO to decide how to handle each one accordingly.
Articles 4 and 5 are rarely used partly because they send very strong signals that may not be the most appropriate course of action. Deliberate escalation is not generally considered a fitting immediate response (as agreed in Article 1) unless in extremis.
As for deniability, an aggressor can deny all they want, that wouldn't necessarily prevent NATO from offering, for example, security assistance to the victim. If memory serves correctly, the USA invoked Article 5 after 9/11 before an enemy had been identified, so I don't think denials would necessarily confound the Treaty.