Can a castellated PCB/module have electrolytic capacitors in it?
You should look at the reflow instructions in the datasheets (or elsewhere) for the capacitors you are using. The datasheets for at least some of the aluminmum electorlytic capacitors from Nichicon say that the reflow should be done within 2 cycles.

If that doesn't suffice, then you should just contact the capacitor manufacturer directly. Nichicon has a note that says to contact them if the reflows conditions going to be different than what is written.

The remainder of what I am about to say is second hand information taken from a response here:
Is it safe to repeat reflow soldering?


Lelon says something similar and also says do not attempt 3 reflows.
Murata specifies a total accumulated time for reflow instead of the number of reflows.