Through backwards compatability...

[bigfatcarp93]

...is there ANY way I could conceivably play FR/LG, HG/SS, and OR/AS all on the same machine?

I tried looking it up and asking on Yahoo, but those sources have thoroughly failed me, and now I must return to you, pleading for help, Escapists.

 

[Bellvedere]

Nope. 3DS games (Gen VI - ORAS) can only be played on 3DS which doesn't have backwards compatibility for GBA games.

Gen III games (FR/LG - GBA) can be played on GBA, Original DS and DS Lite (the DS systems with a GBA slot).

Gen IV games (HG/SS - DS) can be played on DS and 3DS.

You'd need minimum two consoles. Additionally you also wouldn't be able to trade Pokemon directly from HG/SS to OR/AS (you'd first need to trade to BW/BW2).

 

[Roxas1359]

You'd need minimum two consoles. Additionally you also wouldn't be able to trade Pokemon directly from HG/SS to OR/AS (you'd first need to trade to BW/BW2).

Don't forget as well that you'll need the Pokemon Bank to transfer them from BW/BW2 to OR/AS or X/Y. Transfering them into Pokemon Bank is free, but you need the subscription in order to get them out, and that's also only if Pokemon Bank doesn't act weird and call your Pokemon hacked or not. (It's very picky at times, calling legitimate ones fake and fake ones real through what I've seen/used)

OP, as Bellvedere stated, no you will need a minimum of at least 2 handhelds in order to trade up all the way.

 

[Chimpzy_v1legacy]

No, it's like Bellvedere said, you need at least two systems. An Original DS or DS Lite paired with a 3DS will do nicely.

Alternatively, you could also pair a 3DS with a GBA (preferably the SP model). That way you could also play the Game Boy and Game Boy Color games. Not that you'd need to, what with the remakes, but you could if you wanted to.