Not likely (they didn't really have any borders, you know

). But crusades in the Baltic may gain far greater urgency, as I suspect that the Emirate of Novgorod will be doing even more raiding and piracy than in OTL.
Having said that, a Muslim Novgorod will change a lot of things when the full-on conflict comes about; the Dnieper trade route will remain more valuable as long as Novgorod and Constantinople remain in one civilisation (albeit being cut off from Scandinavia will hurt; still, there's fur trade, which we oughtn't underestimate), but the Baltic ports will be much poorer for it. The Hanseatic League might not even form if this situation is preserved. This change in economic balance will favour the Low Countries and England, however; the North Sea ports will prosper.
Things will get really interesting with the response of the western countries here. If both Constantinople and Novgorod are lost early on, the Christendom will either:
a) reach some limited concord with the Muslims (Venice will do this easily), probably averting the Crusades but still putting their lucrative eastern trade routes in a very risky situation which may lead to either or both of the other two situations eventually;
b) attempt to reclaim the key trade cities in the course of crusades. A much more irritating and at the same time useful Novgorod might actually fall to a larger army that would be raised for this endeavour, in which case we might live to see a viable "Teutonic Empire" (Republic, as in the Polish Republic, would actually appear more likely here for a reformed and "statified" Order) in northwestern Russia, while the rest is Muslim. Not sure if any lasting successes against Constantinople are possible, here, but a Latin Empire/restored puppet Byzantine Empire;
c) start searching for alternate trade routes. Earlier Age of Exploration, what can I say? Also, inasmuch as Novgorod will hurt German trade interests, I expect their city-states to be
much more proactive.
As already said, these possibilities will probably all happen at some point; the question is, which will be the most successful?
Some more notes:
- No schism!
- Mongols of the Golden Horde are likely to integrate Muslim Russia more closely, especially if Novgorod is lost. Not immediately, but in the long-term. I think that Turkic and Mongol influences on Russia will be even greater than in OTL; hell, we might even see a Russian Khan replace the Mongol ones in the end. The Rus Khanate will probably be less involved in European affairs (especially if a) Novgorod is lost and b) Lithuanians are kept from advancing too far in by the Mongols), and more in Middle Eastern ones - expect even more and even earlier interventions in post-Mongol Persia and Central Asia, possibly to the point of the Khanate stretching well into India.
- The German Age of Exploration and the Rus Khanate are not at all incompatible, ofcourse... As both possibilities intrigue me greatly, I might make a map after doing more research.