Well the big difference between a 3rd overtone circuit and a fundamental circuit is that the 3rd overtone circuit contains a high-pass filter to stop the fundamental mode happening. So if you have a 3rd overtone 44.545 MHz circuit, it will be filtered to stop the crystal oscillating at around 15 MHz, the fundamental frequency.
As the 44.545 MHz fundamental crystals won't have any resonance lower than 44.545 MHz, it isn't necessary to prevent lower frequency oscillation, but it doesn't hurt to prevent it and the circuit should just work.
Just remember that a 44.545 MHz crystal is around 37 μm thick, and is made out of quartz, which is about as brittle as glass. The crystal can only be supported at its edges, so you are not talking about a robust item.
The Mouser / Digikey part is made by CTS, and has a load capacitance of 13 pF, and a maximum drive level of 300 μW. The ESR is anything up to 30 Ω. To keep below 300 μW at 30 Ω, the current must be less than around 3 mA. If the load is 13 pF, that means that the crystal impedance is around 300 Ω, and you should keep the voltage across the crystal to 0.8 V rms (2.33 V peak-peak).
It would be better to keep the power down to 100 μW, and that calculation depends on the load capacitance being correct. If your circuit's load capacitance is different, the frequency will be slightly off, and there will be a different impedance.