General Butler:
"I myself reviewed a regiment of colored men in the city of New Orleans, and they were ready to fight for us if we had brought them into requisition."
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Subject is "they", the "colored men in the city of New Orleans" who formed the Louisiana Native Guards Regiment.
"Were ready to fight for us" is the desired or proposed action, emphasis on "ready". We can also read the word "ready" as available. The regiment had organized under Louisiana state militia law. By mentioning at least one review, Butler tells us that this properly organized militia regiment conformed to activities required of all state volunteers. All militia organizations were expected to assemble regularly by company, battalion and regiment for drill, parade, review or other activities directed by superior commanders. Volunteers had to conform to a much more demanding schedule. Without a formal call into actual service, however, these activities should not oblige members to be away from home more than twelve hours on any one occasion.
"If we had brought them into requisition." Subject is "we", the militia chain of command for the Louisiana Native Guards Regiment. The highest level would be General Butler and his boss, the Governor of Louisiana.
"If" is a big word here preceding a condition that applies to the primary clause ("They were ready to fight for us"). "Them" represents the object of the dependent clause (members of the Louisiana Native Guards). They could not enter service on their own; they could only be brought into service (requisitioned) by "we", the higher authority. Except in case of extreme emergency, that must be the Governor of Louisiana. The Governor had final authority to initiate military action in defense of the state and deploy resources and assets necessary to do so.
"Had" means an action competed in the past. The war was over. The LNG had not been called by the Confederate Governor of Louisiana before the war ended. The only way you can read General Butler's sentence differently would be to replace the word "if" with the word "when".
Butler is telling us that the LNG was ready, but "we" never called for them in actual service.
If my explanation is confusing, try this analogy:
"Honey, there probably was a bathroom back there if you had let me stop." Translation: the desired event didn't happen because SOMEBODY couldn't make a decision. My wife needs to go, and she thought the gas station we passed twenty miles ago looked too dirty for her. I don't know when we will find an acceptable place to stop, and now it's up to her to decide if we should turn around and go back. If we don't find someplace soon, it will be my fault.