So you are asking if it would be possible for your pseudo-Muslims to launch a religious crusade against psuedo-Europe... And succeed for some time, conquering much of pseudo-Europe possibly until they are stopped by a single kingdom?
Have you ever heard the story of Charles Martel (The Hammer)? First kings of all of Francia? Also referred to as the Savior of Christendom. Grandfather of the first holy roman emperor (Charlemagne)?
A long, long time before the crusades. An Islamic country (Umayyad Caliphate) set out on a war of religious conquest against Europe, they nearly succeeded. Conquered all of Iberia (Spain for you heathens) and half of Gaul (France). Its quite possible all of Europe would be Islamic to this day if not for Charles Martel. Who defeated the Caliphate forces at the Battle of Tours with an army of veteran infantry he had spent 10 years training for the purpose of taking control of Francia, and specifically to beat back the invading Arabs. He even secured a loan from the pope to help him maintain the army... Crack open a history book and read about it, it is a fascinating and apparently forgotten piece of history, you can get an overview from Wikipedia.
Enough with the history now to answer your question.
- Is it viable? Not only is it viable, it actually happened In fact you could say that the crusades were a reverse of the Islamic invasion of Europe.
- Would they be welcomed as liberators? No... As the historical precedent shows that they did exactly the same atrocities to the Europeans that the Europeans later committed during the crusades... This does not endear you to the natives.
- Would the crusaders liberate those poor peasants from the evil oppressive hierarchy of feudal Europe? No, if anything this invasion will reinforce it, as the peasantry will see how their feudal overlords fought and died to save them from religious oppressions and zealotry of the heathens. Prevented them from being raped, and sold into slavery, acted as the guardians of Christianity. (At least that is what happened historically, and feudalism came about as a result).
- Difficulties they would face:
- Cold weather, if they come from a hot climate, they wouldn't have cold weather clothing.
- Inferior armor their armor will have been designed for hot weather... The pseudo Europeans will have significantly heavier and better armor. Their man-at-arms would wear better armor then the most heavily armored foreign invader, and would be able to walk forward thru a hail of arrows to stab impale said invader thru the gut (European knights during the first crusade dressed in chainmail were shot with arrows until they looked like porcupines, and butchered anyone who fought them hand to hand).
- bad bows. Rainy weather, and hot weather allow for different bow technologies... If your invaders use composite bows they will slowly fall apart because of the heavy moisture.
- Sick elephants. Elephants (And horses) don't like ships. Elephants are also not a cold weather creature, and will probably succumb and die to disease during the winter from the cold much like Hannibal's elephants did.
Why do I say it will be like this?
In the middle ages, armies did not have supply lines. Armies had foragers.. Foragers would go to the surrounding countryside and "obtain" supplies to feed the army from it. Peasants who complained about their cows being killed and their crops stolen/ trampled underfoot were "silenced" (killed). Rapes also occurred. European armies did this when they invaded, Islamic armies did this when they invaded. That was the entire purpose of Scandinavian raiders...
It wasn't until the invention of canning (Napoleonic era) that it really became possible for armies to have supplies shipped to them over long distances. And even that was pretty limited... (Armies eat a lot).
There are some armies that are exceptions to this... For example the steppe tribes brought most of their supplies with them (Despite that, they still pillaged) in the form of horses (Meat, milk, blood)... But horses don't like travel, and that relied on the fact that grass grows on the ground, so each steppe tribesman could bring along a string of horses... Grass doesn't grow on the ocean. Which makes transporting horses across the sea much harder.