Can I safely use a supply like this with both the L and N being at 120v with only the ground as a neutral?
No, NOT "with only the ground as a neutral". With the ground as Ground!
To reiterate this point, and answer the actual question asked:
If you have a 3-wire 240VAC circuit (live, live, ground), you can connect an appropriately rated switch mode power supply by connecting the two hot wires to "Line" and "Neutral" on the power supply, and connecting the green/yellow safety ground wire to the "ground" terminal on the power supply. The fact that your "neutral" is at 120 VAC relative to ground doesn't matter.
Do not connect the green safety earth to anything labeled neutral, doing so defeats the purpose of the ground wire.
In the past, it used to be allowed for high power appliances (electric dryers and ovens) to use the same wire for neutral and ground, using the "ground" wire to return a small amount of current to run 120 V control circuitry. This hasn't been allowed in new installations for many years, but many examples of it still exist. When done properly it wasn't the _worst_ thing ever -- the current was small, the wires were large (to handle the potential fault current form the high power circuity) which made them both low resistance and physically robust. The nature of large appliances was that the cables were not usually exposed to much wear and damage and the wiring was a single run back to the breaker rather than stopping at multiple outlets with wire nuts that could get removed. So a neutral fault that resulted in a live chassis was very rare but it is much better to use the dedicated safety earth as is now required.