It's a good question.
I have seen loads of vintage press photographs for sale with many stamps and notes on the back, and I don't recall seeing any bleeding through the often very thin fiber paper used in those days. I doubt archival longevity was a concern when choosing ink, but yet it mostly worked out - it seems.
However, I would not personally stamp the back of a photograph without a good knowledge of how the paper and ink would interact.
When I teenager in the 70's, I stamped my name on the back of my prints. It was Multigrade RC prints so ordinary paper ink didn't adhere and I used a permanent marker pen as "ink pad" without regard to archival properties.
With RC being plastic it is probably not a surprise that the ink didn't migrate through the "paper", but sometimes I have seen permanent marker ink migrate into plastic materials so I consider myself lucky.
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