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How important is it to you that a model's base be the GW-supplied one (I say GW only because I don't know if other game systems care about it)?

Example: I'm doing up some Rough Riders for my Imperial Guard. Now, I'm supposed to use the GW cavalry bases. But I've seen some nice work done with RR units on 40mm bases. It just looks better, and the model is more stable to boot.

Would you have an issue with these guys at a GT or similar event?

A GT maybe, there will always be someone to bust your chops. Local and RTT it shouldnt be an issue. Even more so if they are painted nicely.

Even more so since the Forgeworld models are provided on 40mm bases
http://www.forgeworld.co.uk/Warhammer-40000/Imperial_Guard/Death-Korps-of-Krieg/DEATH_KORPS_OF_KRIEG_INFANTRY_AND_ACCESSORIES/DEATH-KORPS-OF-KRIEG-DEATH-RIDER-4.html

Thank you for pointing out the DKOK example! I feel like that would vindicate me using them.

No particular need for vindication. Just run them past the TO before the event, and so long as you have their ok, there's not much that anyone else can say about it.

Get some Calvary bases and if someone bitches plop down the empty bases. I used to do that before rebasing my termis.