I suppose it depends on the LDO and the proposed input to the LDO.
I think most just turn off when they hit the current limit (not what you want). Others just stay fixed current until the strong load is removed (this is what you want).
Another option might be to use an adjustable LDO that takes an external reference. You can then slowly ramp up the reference with a dv/dt that limits max I for your C. You have to be careful with this though because at the beginning there will be lag on the output and the error signal could cause the LDO pass element to saturate, which would likely blow it out (depending on how much C were talking about).
What were you planning on using as the input to the LDO, about how much C is in the bank?
Another, possibly better option (assuming the reason you want the LDO is to make a precise voltage on the cap) would be to over charge the caps on purpose, then remove that power source, and finally slowly bleed off the excess charge with a weak parallel R. Remove the R when the right voltage has been obtained.