I would be surprised if the switch is allowed. I don't know all of your particulars, but there are some noticable differences in the two specs:
A992 states open-hearth, basic-oxygen, or electric-furnace. Additional
refining, by electroslag remelting (ESR), vacuum-arc remelting (VAR), or ladle metallurgy furnace (LMF) further, the steel is required to be killed.
A588 states open-hearth, basic-oxygen, or electric-furnace and the steel shall be made to fine grain practice. The open ended statement of fine grain practice does not always mean killed.
A992 has a specific tin allowance of <2% while A588 has nothing of the sort
They vary for chemical allowances as well.
A992 has a higher carbon, differences in Maganese, depending on the grade of 588 a lower allowance for silicon, depending on the grade a lower nickel allowance, in short several chemical allowance differences.
Depending on thickness, for the most part A588 has lower yield strength and other differences in mechanical processes.
I am not a coatings expert so I cannot answer that part, but judging from the variances in manufacturing, chemical, and mechanical tolorances and methodology, I would not suggest making the substitution.
It depends on your application. If the design relied on the particular yield-to-tensile ratio that is required in A 992, then you can't use A 588. For most structural applications, though, they're fairly equivalent. If old A 572 would have sufficed, then A 588 ought to be fine.
Hg