Well, there's a lot of different mic types, but here's a few explanations:
First, many dynamic mics produce so little voltage (Shure SM57/58, Senheiser 412, AKG D12, etc) that any induced noise is significant compared to the signal. A step-up transformer makes the voltage HIGHER in these cases, while not making the impedance too ridiculously high.
Tube condenser microphones on the other hand frequently produce larger signals at the anode or cathode of the tube, so the signal-to-noise voltage ratio (in terms of surviving a long trip down a mic line) is pretty good... however, the impedance might be too high for even moderate length cables (the higher the source impedance, the more high end is lost to the inevitable cable capacitance, which increases proportional to cable length). -In addition, the tube produces a single, unbalanced signal. A transformer also has the wonderful benefits of galvanic isolation AND balancing.
Now, for phantom powered microphones, the simplest circuits are something like the KM84, where a single FET is used in a comparable way to a tube in a simple tube mic. It produces a single unbalanced output signal, and the transformer effectively balances the signal, as well as tweaking the impedance to suit the typical range of mic preamp loads.
Now... on to transformerless mics:
There ARE transformerless tube designs. You don't encounter them much, but they do exist. -A friend of mine builds all of his this way. With these, you do have to be mindful of cable length.
Many designs however (like the much-imitated Schoeps), produce a differential output signal which is itself essentially balanced. Therefore part of the 'need' for an (expensive when done right) transformer is suddenly less pressing.
In addition, they use fairly low-impedance drive circuitry, which is capable of driving longer lines with little loss of high end (in the case of many transformerless Chinese mics, a little HF rolloff might actually be a NICE thing! -although that's a personal taste issue, of course).
Some transformerless mics produce an unbalanced signal, but use the 'silent' pin (from which they still draw half of their phantom power current) as a matched-impedance connection to ground, which allows most balanced-input mic preamps to still cancel noise fairly effectively.
-So there are a few designs out there, and they can work QUITE differently, but off the top of my head, I'd say that the only transformerless mic designs that spring to mind which WOULD be particularly sensitive to long lines are the transformerless cathode follower tube designs which I've seen... and they're not a common topology, in my experience.
It's a good thing to ask however. -While I'd say that most mics manufactured for general sale have been engineered to be capable of driving fairly long lines without great problems, there may well always be one which catches you out!
But as to whether being 'transformerless' has any automatic bearing on ability to drive long lines... I'd say basically that the answer is no.
Hope that helps more than it confuses the issue!
Keith