What range are you wishing to achieve?
If I increase the voltage from 5V to 12V using a boost converter, or a charge pump, would that have the same effect as having a 12V supply in the first place?
Yes. as long as the supply can provide the required current the transmitter does not "care" how the 12V is provided.
Can the RF TX really draw more power through a boost converter?
It can really draw more power with more supply voltage - whether from a boost converter or otherwise.
RF can have more output voltage than supply voltage due to resonance but an order of magnitude check of result is often useful. A 12V rail to rail signal = +/- 6V. RmS value is 0.7071 of that or about 4.2V. Say 4V.
Power = V^2/R and R = V^2 / Power
To get 32 mW at 4V then Rload = V^2/Power = 16/.032 =~~ 500 ohms. As typical antennae used with such devices are liable to present impedances of 50 ohm or 75 ohm for whips or dipole or 300 ohm for a folder dipole. Either way, there is enough supply voltage at 12V to meet the 32 mw spec.
If you want substantial range you are liable to get best return for effort by implementing a formal antenna (ie not just a random untuned piece of wire of unknown characteristic), driving it well (impedance matched, low VSWR). If you need more than what simple whips etc will easily provide you can implement multi element "beams" or cantennas with relative ease. 432 MHz is a bit low for good gain cantennas but you are unlikely to need much.
432 or adaptable:
Quadri Filar and here
Skewplanar - from here includes dimensions for 432 MHz.
Mainly 2.x GHz - things to learn:
Oh Yes !!! :-)
The photo below is from this page which is all in Arabic unless you allow translation, when it's 98% in Arabic and the gear shown is largely aimed at 2.x GHz BUT it's very worth looking at regardless.
[They seem to think they know what they are doing :-) :
Or in Turkish - not as good. 2.4 GHz
Spanish 2.4 GHz excellent
The aerial with a rod with circles twisted in it can be adapted to 432 MHz.
2.4 GH - v good