These things are not only possible, but commonplace today. Just because a microphone can be driven with standard 48-Volt phantom powering doesn't necessarily mean that its circuit requires (or even uses) 48 Volts as such.
When DC voltages higher than the supply voltage are needed in a microphone, a "DC converter" can be used. This type of circuit (also available as a prepackaged component) takes a given DC voltage and uses it to drive an oscillator, at a frequency which, in audio circuitry, ought to be well above the audio range so as to avoid interference. The high-frequency AC can then be stepped up to a higher DC voltage either with a tiny transformer (followed by a conventional rectifier and filtering), or with a diode-and-capacitor network called a "voltage multiplier" (plus filtering).
DC converter circuits reliable enough for professional microphones started to be possible in about the early 1970s; older designs avoided them with a few notable exceptions, but newer designs use them a lot.
Condenser microphones may have pre-polarized diaphragms (i.e. electrets) or they may be "traditionally" polarized with external DC (or a third option, which isn't so relevant here, is to use the diaphragm and its backplate as a variable capacitor in a radio-frequency circuit). The Rode microphone is most likely an electret, which means that it doesn't need any high-voltage DC to polarize the diaphragm of the mike; it only needs enough to run the FET impedance converter circuit which drives the output. Again, that might be obtained by stepping up the 1.5 Volts of the battery to, say, 5 Volts, which should be more than enough for the audio circuitry.
Historically, 48-Volt phantom powering was devised for use with capsules that had been used in tube microphones with 60 Volt polarization. But even when you are feeding 48 or 60 Volts to a capsule to polarize it, the capsule is, after all, a capacitor--which means that once it is charged, no more current flows into it from the supply, except to replace whatever is lost from leakage. The usual audio-frequency circuit has this voltage applied to the capsule by way of an extremely high-value resistor (hundreds of megohms to a few gigohms), so the amout of current is absolutely miniscule. As a result, a DC converter can easily generate enough output to polarize the capsule without drawing much current from the preamp. The main consumer of power is the output stage of the microphone, which is usually class "A" circuitry (in which the output devices are always conducting).
I hope this also answers (by implication) your question about the preamp that can run from a 9-Volt battery and yet offer 48-Volt phantom powering. In a way, the arrangement is a little inefficient because 9 Volts is being converted to 48 Volts but in many cases (e.g. Neumann, Schoeps, and some AKG mikes) the microphone takes that 48 Volts (or the somewhat lower voltage that it actually receives, since when current passes through the pair of 6.8 kOhm phantom resistors, the voltage drops in proportion to the amount of current being drawn), drops it to some lower voltage with a Zener diode, and then runs that into another DC converter, e.g. to get 60 Volts to polarize the capsule.
Does this help?
--best regards