If I get what you're saying, then no they wouldn't have to actually do any sort of resizing of the layers, doing so would actually be detrimental as you'd be able to "peek" around the layers (since foreground layers scaled down to be the same resolution would leave holes around the border and wouldn't fit the screen)
If you mean, by the simple fact of having the layer "closer" than the last one would make it appear larger, then yes it would likely trim a few pixels off of the side, which would be a non-issue in nearly every game as long as you had the HUD in the right position (this would be the only layer where it would be appropriate to scale it down to fix the screen, I know at least one DS SNES emu can already do this, the downside of course would be for games where the HUD layer shares actual gameplay elements, but those are the exceptions and not usually the rule)
(edit) To expand out on this, you have to remember that SNES games are also a lower resolution than the 3ds, even if you take into account aspect ratio (256x224 is the standard game res, though there are a few other graphic modes the system does support, including a 'hi-res' 512x224 but that's only used on a few games and mostly only for displaying text in certain RPGs. Because the SNES has a lower resolution, the upper layers being slightly enlarged from being closer to perspective actually works to the advantage of the system, able to fill in the rest of the screen real estate while only having to deal with the pillar boxes.
We're probably talking on each layer the difference between a couple pixels, this will undoubtedly lead to a little blurring but it should be managable and in most games wouldn't require much adjustment (objects on the top layer overextenting the lower layers)
The only other solution would be to have the actual system render at a higher resolution than the SNES actually supports which would be impossible via emulation... What you'd be talking about then would be porting the games and, most likely, reworking their entire engines which would be quite a task just to bring a 20 year old game to the portable with 3d effects... It's not like today where game systems all had fairly similar SDKs and used common programming languages, the NES/SNES/early N64 days Nintendo used very proprietary programming languages that were much lower level and don't port easily... It wasn't till the late N64/GBC/GCN era that Nintendo made the switch to C as their primary language for their SDKs.
(edit 2) forgot to mention something... nerrelferrel: That scene is composed of only a single (maybe 2, been too long since I played it last) so while it would definitely stand out, it's not going to be a shower of all different levels of depth unless they did some manual tweaking of the scene.