Thanks for passing the buck.
I don't think that an absence of the war with the Ottomans in 1806 would have a critical impact on the events elsewhere. In 1806 Russians had approximately 40,000 troops advancing into Moldavia and this number increased to 80K only after Peace of Tilsit. Of course, if we assume that all these extra 40K had been present in East Prussia by the early 1807 then one may speculate about a possible outcome of the Battle of Eylau: instead of an approximate parity of the numbers Bennigsen would have approximately 110K vs. 75K French. This, of course, involves a lot of "IFs" and does not address his questionable ability to develop a field victory into a strategic one (Bennigsen was an experienced and capable general but he clearly had his limitations on strategic level). As an additional food for thought, AFAIK, during that campaign both sides had been suffering from food shortages so how these extra 40K would be supplied is anybody's guess.
Anyway, my understanding is that on this stage of the War of the 4th Coalition Napoleon had general advantage in the numbers at it would be mostly an issue of him bringing these numbers to the front while Russian army of that period did not have big strategic reserves. And, of course, it did not have Napoleon. So, IMO, the chances to defeat Napoleon (as in "winning a campaign") would be extremely slim no matter what.
As for the invasion of Russia, it was years away and in 1812 he invaded while Russia had a bigger and better organized army than in 1807.