Short answer: Legally, they probably did. In practice, they said they didn't. As war broke out, the issue was never adjudicated.
Discussion:
With the Anschluss, Germany got the reserves of the Austrian central bank, and could pay for Austrian resources in Reichsmarks (which were not easily convertible at the time).
In the Austrian National Bank the Germans found gold worth 240 million schillings. This they at once removed to Berlin. They furthermore came into possession of Austrian deposits abroad, valued at around 16o million schillings, as well as some 300 millions of foreign securities held by Austrian investors all of it subject to forced sale to the Reichsbank. Germany thus gained the equivalent of approximately half a billion reichsmarks in gold and foreign exchange. This sum is considerable in comparison with what the Reichsbank previously had at its disposal. But it will alleviate Germany's foreign exchange troubles only partially and temporarily. If German imports of foodstuffs and raw materials for non-military uses were to be restored to their normal level, this new treasure would last hardly six months. Therefore, either the newfound wealth will shrink rapidly, or difficulties in obtaining food and primary products will continue.
Incidentally, it also should be noted that Germany's foreign debt will be increased by some 1,300 million marks- that is, if in the end she assumes Austria's obligations in full.
The Nazis rejected the idea of responsibility for Austria's external debts
German Reich Minister of Economics, Herr Walther Funk, made a speech at Bremen (June 16) [1938], in which he emphatically rejected the validity of this proposition and asserted that "neither by international law nor in the interests of economic policy, nor morally, is there any obligation on the part of the Reich to acknowledge the legal responsibility for Austria's Federal debts."
[T]he reasons relied upon by Minister Funk in defense of Germany's irresponsibility for the Austrian debts, fall into three groups: first, the inapplicability of the rule of state succession in the case of the self-extinction of a debtor state; second, the "political" character of the debts, which, in his opinion, removes them from the category of legal obligations to which the law of state succession applies; and third, the existence of certain historical instances in which other states, notably Great Britain, France and the United States, declined to assume responsibility for the payment of the debts of states which they had conquered or annexed. If, therefore, according to the Minister, it was permissible for them to repudiate the debts of states which they had annexed, they cannot justly complain if Germany now adopts the same policy in similar circumstances.
In his 2001 study of Germany's foreign exchange balances (which were substantially a secret at the time), A. O. Ritschl finds that between 1938 and 1940:
The evidence collected here seems to suggest that the autarky policy of Nazi Germany may not be readily interpreted as a general withdrawal from international trade in preparation for war. What it shows, instead, is a drive for partial disengagement from Germany's dominant creditor countries, along with the attempt to build up import-substitution industries in the fields of maximum dependence.
That is, Germany was trying to "pick and choose" who they did business with and on what terms. They were not a fully self sufficient autarky, but in the limited interval between the Anschluss and the outbreak of War in September 1939, they were essentially doing everything to buy what they needed and pay out as little hard currency as possible. Their repudiation of Austrian debt might have become a subject of diplomatic controversy, had not a shooting war broken out.
Sources:
The Austrian Contribution to German Autarchy 1938 article: this is what the west knew at the tame
Germany's Responsibility for Austria's Debts another 1938 article, this from The American Journal of International Law; the author identifies the legal defects in Funk's position, remarking in a dry lawyerly tone that Nazi policy of repudiating the principle of succession of debts "will be a matter of regret"; eg that the Nazis might later find it not to their advantage. As it happened, this didn't matter much as bigger events intervened.
Nazi Economic Imperialism and the Exploitation of the Small: Evidence from Germany's Secret Foreign Exchange Balances, 1938-1940 2001 article in the Journal of Economic History; important data from Nazi secret economic files, which were later discovered in West Germany's National Archives. Excellent bibliography for further reading, if you're working on the subject.
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