Again we are putting together fiction from whole cloth. I have never heard of any such movement described here through France and it is still a year short of D day. And we should have heard of it.
Those magic giant subs do not exist either and are an unnecessary addition. The problem is simply hull strength and the technology needed to produce such a craft. We do not go there today. It did not happen.
Better yet, movement by sea from neutral Spain by merchant ship to the Argentine is viable and hardware can go as well. Any such contingent plan would have used that route and naval intervention would have been unlikely in 1943 because all available resources were fighting the convoy battles. And do you really think that anyone would care too much if Germans and resources were on a trip away from the battle front?
Anyway, at best it would have been plausible to send out 5000 to 15000 people in this manner and certainly not 250,000 even if they had magic subs. That also suits the known facilities available to them in South America at the time. Much more that that and security would surely have broken down.
This route slammed shut in the late summer of 1944 after D day. Later escapes were few and done by air.