Yes, I believe this is possible to implement without “messing up” the established world as long as there are limits to its implementation and the factors below are addressed.
First of all, any train would have to use old technology, and I mean OLD, by not even using a steam engine. Rather, have a couple of Golems (or similar “creature”) use a simple mechanism like a handcar (which is also used in mining, so the idea is even less far-fetched). Also, the availability would have to be severely limited (no subway stations).
Land: This will be the biggest hurdle and probably the biggest expense unless the land is granted by “the government” (I think they would like to allow the investment in their infrastructure as it can only benefit them if this takes off)
"Fuel": Since we are not using steam or other fuel then we are relying on manual labor. The price of Golems is not cheap, but it is one of the most stable with no additional costs, but we are talking a hefty investment just for our “fuel”.
Labor: Once you have the land you still have to lay the tracks on them..this will be no small endeavor. However, I think that if the King (whoever) has already granted use of the land, they may be willing to allow the use of prisoners for labor. (Ofcourse this is assuming slaves do not exist in the kingdom, for those that do this may be a different issue) However, even if you use prison labor you will still have to hire overseers/guards etc to make sure they stay in line. And you’ll have to provide them food/bedding etc.
Raw Materials: Once you’ve acquired everything above you still need raw material to build the tracks with & ofcourse the actual train cars. This will be the smallest of the large expenses but still a large one to consider.
Routine Maintenance: Not as large as an expense, but all mechanical things break and must be fixed, so it does exist. This expense grows if we run into any of the “problems” listed below.
Problems: Assuming you’ve overcome all the financial/logistical hurdles to build the thing there are still numerous problems with having trains run.
Most obvious will be bandits & monsters/creatures(dragons?) who try to rob the train. The train would have to employ any number of guards to protect the train & passengers. However, merchants would still be required to hire their own guards to protect their wares. Nobles, likewise, would be advised to hire their own guards to protect them in event of any “trouble”. While it might seem unfair to have passengers/merchants pay for their own protection, they would have had to do this for a normal convoy anyway, but the ‘bonus’ now is that they won’t need them for as many days. Besides(Release forms for their safety/wares would have to also include a clause about “unavoidable delays”.)
Tracks, once they break the tracks the train will have to stop (if it doesn’t derail).
Measures taken to address problem: The train will have to have several cars devoted to spare parts to repair the tracks along with the labor to complete the work.
Bridges!!: This risk is so high/expensive to repair that I think it completely negates their use at all; unless the trains/operators have been around for so many years that they can afford all the VERY EXPENSIVE magical protection to protect them. However, there will always be someone powerful enough to overcome their protection which will make the loss of this bridge even more disastrous; not to mention that there will not be enough labor/parts on hand to rebuild a bridge on the train itself.
Measures taken to address problem: This problem is so expensive/dangerous that it must be left out completely. Any place that would require a bridge simply cannot be traversed by train.
Old fashioned train robbery: Even without damaging the tracks people could still go the old west route and do a direct attack by catching the train in transit. While this made since in real life, in a world filled with magic I think this would be ridiculous.
Measures taken to address problem: As stated, this option would be ridiculous, and can be protected against with the guards on hand.
Kill the “Fuel”: This would require the attackers to board the train in one fashion or another, but once on board, a small 2-3 person party with enough power could kill the Golems making the train run turning it into a giant, expensive, lucrative target.
Measures taken to address problem: In addition to the Golem’s own defenses we will need guards solely to protect the golems; a possible anti-life field around the “locomotive” portion of the train will be a very effective, if very expensive protective measure as well. (Logistics on fixing broken mechanical pieces will have be more difficult, but not impossible).
This would be a VERY expensive endeavor, and the customers would have to pay a pretty coin for this option. Additionally, by paying for their own guards this cost is increased significantly. This would make the “pool” of potential customers shrink significantly meaning it would be even harder to recoup investment costs, let alone turn a profit. Due to the extravagant expense of making this happen, I don’t think it would “mess up” the economy.
Note: I tried to make this answer as “clean” and readable as possible. I think I’ve gotten it pretty good, but if anyone feels they can make it read better, without removing any of the points, then that would be fine too.