Everything else equal, I think it does.
Let's try another experiment (requires a brickstone house)
Go out in your garden place a brickstone in a suitable distance and shout at it.
Turn around and shout at your house's brickstone wall.
Which action do you think produces the greatest echo?
The reason I stated that the experiment you suggested does not correlate to the submarine size question is that in the plate experiment, you were using two differently sized plates, of the same material. With two differently sized submarines, the chances of them both being built using the exactly same material is slim to virtually none. In addition, the type and layout of machinery is going to be different between different classes of subs, as is the internal and external shape and fittings.
Where one can run into a size limitation is that there is potential for certain types of acoustic reduction to require a certain size/volume/mass in order to be efficient and/or effective.
As an example of what I mean, I present the W.A.G. Institute-created material Rubbermaidium®
It is a material which has a weight of ~1g per cm^3, and when applied to a submarine hull in layers at least 50 cm thick, can reduce the acoustic signature (at least for certain frequencies) significantly. In short, if one is willing to add 'dead' weight onto a submarine, as well as increase the overall width of the hull by 1m, then Rubbermaidium® can be used. As a result, such a material might be better and more easily utilized aboard a larger submarine, because a potentially lower overall percentage of the submarines mass and size/volume would be taken up by the Rubbermaidium® layer.
Incidentally, it is not true that diesel submarines are automatically smaller than nuclear submarines. The French
Rubis-class SSN has a surface displacement of ~2,400 tons, while the RAN
Collins-class SSG/SSK surfaced is ~3,000 tons and the Japanese
Oyashio-class SSG/SSK is ~2,700 tons surfaced.
As a side note, the reason why a diesel sub on batteries can be quieter than a nuke boat is that the diesel can potentially turn off all onboard machinery for periods of time. A nuke boat always has to have machinery running to maintain the reactor. These pumps, being mounted within the hull of the nuke boat create an acoustic signature, just like every other moving or mobile part of a submarine.
-Cheers