I think that when we take into consideration any decision by a competent expansionist power (as the Ottomans undoubtedly were during this period), there are probably several main elements that dictate whether or not they will attempt to conquer any given territory:
Balance of accounts: This has to do with whether the presumed cost of the conquest outweighs the economic benefit derived from the incorporation of the territory into the Empire. This value will derive itself from several sources. First of all is tax income, which also includes the jizya. Despite the increase in tax burden on the people resulting from the jizya, this is only useful if the locals are capable of paying it, which I think is probably questionable in the Russian case. Farming techniques are backward compared with much of the rest of Europe. Russian territory is open and with poor infrastructure, creating a significant burden on tax collectors, with little control over the accountability of tax collectors, who may well skim plenty off of the top for themselves. A tributary relationship, receiving furs, possibly amber or other goods that are scarce in the Eastern Mediterranean, is more valuable, and to a degree operated IOTL with the Crimean Tatars as a middleman providing Russian slaves.
Capability: The ability to project power in order to seize and maintain control over the territory. At least in regards to the former, I have little doubt that the Ottomans could have maintained control at least over large territories in Ukraine. In the late 1600s the Ottomans were able to impose their control over much of Ukraine, including authority over the Cossack Hetmanate, until Poland and Russia began to unite against the Turkish threat. This is where the second problem comes in - retention of control. I highly doubt that the Ottomans, who face multiple significant rivals on different fronts in the form of Safavid Persia, the Hapsburgs, Spain, Poland and Russia, can retain control over wide open areas such as Russia without the complete annihilation of the relevant threat in a particular theater and the establishment of borders along natural barriers. In Russia, this is simply not possible. I can't see an Ottoman Empire capable of exerting the effort to seize all of Russia west of the Urals without opening itself up to the dispossession of their core political and economic powerbases.
Relative Benefit: This is whether or not an alternative target for expansion can provide a more immediate and significant benefit to the conqueror. This is definitely present. Italy is far more likely to pay dividends, having a highly-developed economy, numerous rich cities with a high tax base, lots of infrastructure allowing effective tax collection and trade, easy access (as long as naval superiority is maintained) and defensible frontiers (the Alps). With this added revenue, I could see the Ottomans being able to seize Vienna and maintain a line between the Alps, the Leitha Mountains and the Carpathians. They could easily fortify the passes along these lines and make an extremely formidable line of defense between Ottoman Southern Europe and the rest of the continent. With the added revenue of Italy, as well as more ports and expert shipwrights, they could likely achieve supremacy, if not outright dominance over the Mediterranean. Between a powerful Ottoman fleet in the centre of the Mediterranean and the Barbary pirates, it would be extremely impressive if the Spanish and the Knights of St John were able to roll back Ottoman strength. It is even possible that the Ottomans would be able to utilise their wealth and power to keep the Protestants and Catholics divided in Germany, and could ally with the French at the expense of the Spanish. It is true that in such a situation, a Russia which extends its control over the Ukraine is the only real single existential threat to the Ottomans. There is no easy fix to this. I would presume that there would need to be, after all of these Danube and Italian campaigns, an effort to balkanise Russia and support the Crimean Tatars. That being said, there is no easy fix, and for an Ottoman ruler accustomed to their own supremacy, Muscovy would seem like a very distant threat indeed. An expectation of such foresight is probably unreasonable.
Based on balancing these factors, it seems unlikely that the Ottomans could hold significant Russian territory for an extended period of time.