Seems rare that they measure, especially squishy bags that aren't obviously way oversize, where the dimensions are a little fuzzy anyway. A footlocker type thing might invite measurement (and other attention), but if it's ok it's ok.
I'd worry more about weight, if you really want to try this I suggest a dry run well before your trip. And the durability - plastic box type things are prone to cracking when they get dropped or whatever, unless they're made for that sort of abuse - in which case they'll likely be heavy enough that it's hard to imagine getting 1-2 sets of gear in there and not be overweight, never mind 3. For regular dive gear I'd stick with regular luggage of some sort. Rolling duffles like the one RoatanMan suggests work well. We have Eagle Creek ORV trunks that are similar, though no backpack straps.