...because of ideological or pragmatic reasons?
Did the bouts of positive relations that occurred between the French Empire and the Austrian and Prussian and Russian Empires (& Vatican) happen more because, in proclaiming himself a monarch (and concordat with the RCC), the French regime became less anathema to those other powers, or more because at those moments it was just too demonstrably costly to *not* accommodate Bonaparte, send a daughter to marry him, etc.?
IF we accept the pragmatic explanation, then it seems that although the Republic was militarily formidable, the other powers and the Church could *afford* to be unalterably opposed to it. However, the what-if implication is that if the Republic (whether under a Consulate or a Directory) became as militarily formidable as the 1807-1812 Imperial France, the powers would have made at least temporary deals with it, too.