It will smooth it out a lot, but to get it absolutely flat you need to float on some SLC (self levelling compound) over the top of the ply. If I were you I'd use a long straight edge to see how far off you are now, and make my decision then. Remember that if you do overply it is ring nails on 100mm centres (325 per sheet) or screws on 150mm centres with 100mm centres around the perimeter (about 180 screws per sheet). There are no shortcuts to this
A power planer can thin down boards quite quickly, but nails and screws need to be set beneath the surface first (and checked for regularly) and even then you'll hit a few, so best to have so.e spare blades available. Limit the amount you take off, though - on old 1-1/4 to 1-1/8in (32 to 28mm) boards you can generally take off 5 to 6mm, but on 1in (25mm) boards I wouldn't take above 3mm, and below that I think I'd give it a miss.
I wish they were 28-32mm boards - they are about 18mm thick that's all. I used a hand plane (hard work) and maybe got a couple mm of material off.
I don't know if I could use SLC anyway as the whole floor appears to slightly slope down front to back. I don't think this is an issue for laminate as long as the floor is flat enough.
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