In fact it didn't "strain" Sora at all. They co-existed perfectly fine until Naminé started messing with his memories, which is actually a side-effect of how she was created as stated in the video.
The reason why she could manipulate Sora's memories is because of how Naminé was created, it didn't have anything to do with Roxas or Xion.
The whole mess however truly started after Naminé had made a mess out of Sora's memories.
The memories sampled by Xemnas gave Xion a basic, rudimentary way to function, but once Sora's main chain of memories was broken due to Naminé and the events in CoM, Xion's inherent ability to absorb "loose" memories from Sora kicked and she proceeded to absorb more and more loose memories from Sora through his connection with Roxas.
Due to that, Roxas suddenly also had memories of Sora (that's why he starts to have these dreams/visions during Days after CoM was finished) and these loose memories where constantly shuffled between him and Xion.
All this is also the primary reason why both Xion and Roxas had to return to Sora at all.
Because so many memories of Sora were spread out between Roxas and Xion, Naminé was unable to piece them back together and separating Sora's loose memories from Roxas' and Xion's own memories (which were used to have their own hearts grow and nutured) would have taken too much time.
When DiZ in KH 2 speaks about "half of Sora's power" he is referring to all the loose memories of Sora that lay within Roxas.
Or in short: Had Xemnas & co. not created Xion with that memory absorb ability and had Naminé never messed with Sora's memory, Roxas would not have needed to "return" to Sora.
Oh...And all this time I thought the reason why Sora was so wonky in CoM was because of Roxas/Xion :U Thanks for clearing it up for me; I have to admit that in CoM/Coded games, I couldn't really understand what was going on because I never played those particular games before (I played CoM, but due to the wonky gameplay with the cards thing, I couldn't get it down right).
But if Roxas never returned to Sora, then it would be to say that Sora would never be getting his 'body' back though. He won't be 'complete', unless the "half of Sora's Power" really are only his memories. I think Sora would function better with both his body and soul back. I don't think this is canon, but in the KH2 Manga, after merging with Roxas, Sora claimed that he felt so 'light' and it was easier to battle. If this same case were applied to the game, then Sora would have never be as good as battling as he is now. Sora showed all those badass abilities in the final battle against Xemnas (CUTTING THROUGH BUILDINGS) that he's never done before might've been from the merging with Roxas. It would've been nice to see Roxas around as a GoL though; not sure how that would've worked out though :I
Well, they showed Roxas battling with the other Warriors of Light in the 3D Opening. Maybe it's hinting how he'll make a comeback. However the only way I can think of Roxas returning is Sora turning into a heartless again (even then I'm not sure it will bring back Roxas, but this is the only known way to 'make' a Nobody) because I've never seen a nobody and the original persona co-exist, save for Xehenort (who presumably used time travel to get this accomplished).