Surely the amount of hydrogen absorped will make no difference to mild steel. Might get nervous with say aircraft "300M" steel fully hardened to "chisel edge" temper, but not "our" stuff - weldable general steel.
Anyway, I've tried hydrogenating steel this way and it doesn't work. I left steel in acids for days, wanting to perform scientific experiments on the hydrogen, and what I find is that there is a hydrogen gas evolution reaction at the surface, as the metal is eaten away, but no hydrogen makes it into the metal. Measured with an accurate hydrogen analyser - got nothing which could be detected to a detection limit about a hundredth of what you get in a low hydrogen xx18 rod.
It's thought the hydrogen is simply cannot get through the state of the metal's atomic bonds at the surface. Hydrogen sulphide (H2S) in the solution does something remarkable - the hydrogen from the evolution reaction can get in then. That's why "sour" crude oil messes-up a lot of steel pipe - it's acidic and contains H2S (the low-carbon zero-pearlite steels made in Europe and Japan and highly immune and satisfactorily cheap).
On the other hand, in the literature, there are investigations (including W. H. Johnson, 1875 and L. S. Darken and R. P. Smith, 1949) where they clearly had got hydrogen pick-up from acids - because they found out all about how hydrogen behaves, so they clearly got the stuff into the metal). Could never work out that one out. Maybe acids in those days had contaminants which had the same effect as hydrogen sulphide - maybe they did contain hydrogen sulphide - it's speculation.
Anyway, believe you don't have to fret about hydrogen pick-up during pickling when the steel is weldable mild steel.