It should work. Your 120v/1500watt elements represent a fixed resistance of 9.6ohms each. Two in series would be 19.2ohms. If 240v is applied across them, they will draw about 12.5amps and provide 3000 watts of heat. 1500watts from each element.
BTW, 240vac behaves essentially the same as 120vac relative to current flow.
In other words, it's a common misconception that the HOT in a 120vac circuit is the "source" of the current and the NEUTRAL is a current "sink or receptor" while the two HOTS in a 240vac circuit both are "sources" of current. This is simply not true.
The current in each leg, (120vac, HOT/NEUTRAL) or (240vac, HOT1/HOT2) is actually the same electrons flowing at any given instant. For half a cycle, current flows from HOT to NEUTRAL & HOT1 to HOT2 and the other half cycle current flows from NEUTRAL to HOT & HOT2 to HOT1.
I'm not sure how one would connect these elements with 120vac gfci's since it depends on monitoring of current in HOT and NEUTRAL for its operation. A 240vac GFCI would work.