The Domaine extraordinaire certainly helped to maintain an oversized field army, pay for prestige works and grant rewards.

Still, 1 billion 1806-1810 was the maximum of the contributions (after defeat of Austria, Prussia, Russia), and covered an average 16% of the french budget for this years. This is significant, but much less than the 84% drawn by the fiscal administration put in place at the start of Napoleon personal power.
More, the war machine kept on functioning without major financial crises from 1812 to 1815, when war required huge increase of fundings, without any additional war gain.

Napoleon may have manipulated figures, but the Restoration had no reason (and no mean) to do so: as stated by Dupont, the total war debt from 1805 was 30% of the budget, and 15% of the war budget, a major debt but manageable - and this is rather a remarkable achievement after three years of military disaster, loss of territories and foreign invasion and contributions;
This debt was cleared in 10 years, thanks to peace, and to the easy selling of loans to french owners' class. This is a sure sign that Napoleon did not bankrupt the state (and that the owners had the 1789 lesson taught: help the government to avoid revolutions).

Also, Napoleon attempted to downsize the army repeatedly : after peace of Amiens, after Tilsit, and after victory upon Austria in 1809. This can be observed in the major increase of officers retirements in 1801, 1807 and 1809.
This explain why Austria could perceive a weakness in 1805 and 1809, when Grande Armée was at Boulogne, then in Spain; or Russia tentative attempt against Poland in 1810-1811, when 40,000 french covered the whole Northern Germany, the remaining being in Austria, Italy, Spain or France.
Austrian and Russian threat in turn led to major increase of french army and invasion of additional territories. But it was rather a diplomatical and military countermeasure than a financial one.

Concerning the economical crisis, peace of Amiens yielded to thrieving economy, the crisis started when overheated expectations were brutally hit by the renewal of the war. In 1810-1811, the crisis was partly indirect result of the Continental Embargo, and counterproductive tarriff policy against German and Italian states t ofavour french products, disrupting the trade circuits throughout Europe; and partly the depressing effect of threatening war against Russia, more than the fiscal burden itself:

As a conclusion, invasion of territories accompanied the increase of french army and Domaine Extraordinaire. But except perhaps Spain, need of additional resources does not seem to have triggered the expansion of the Empire, or major annexation attempts would have preceded, not followed, the wars.

Did the loss of Domaine Extraordinaire decide Napoleon to fight to the end ? There is no testimony to decide, but the consequences of peace were much larger than a fraction of the budget, in loss of prestige, political power, military buffer zones, major economic regions on Rhine and Po,... The public debt being very low in the list.