No, there is no standard for that connection either. I think the one button ones usually work by having the button short the mic pin to ground, in which case any set of headphones which does that will work with any device that expects that, but that doesn't mean any Rockbox player can do it, unless the hardware already has 1) a mic pin for the 4-pole 3.5mm jack used by these headphones and 2) support for detecting that the mic pin has been grounded. This isn't actually any kind of standard, though, and I may be mistaken about how it's even commonly implemented, I've not actually tested such a device with a multimeter.
So basically the answer is the same: This can only be done on devices whose hardware already supports this feature. The iPod Classic and the later Nanos do support this, and some of those players are partially supported in an unstable way by Rockbox, so it would be possible to implement support for that kind of remote on those players only. I don't think anyone has done so yet though; getting stable playback support is more important