Yes.
You will want to eat ACC food by turn 4 (or meld some more ACC) but you will be fine until then.
Refer to this thread for a BC loot table. Unfortunately, MNK body is undocumented and is very likely turn 5. The rest of the Striking set is accounted for.
You can use this chart to compare MNK gear. Keep in mind that it doesn't weigh accuracy as a damage stat, and I don't yet understand how skill speed is weighted. It's a good guideline nevertheless.
