I'm not quite sure what you mean by "surely OBS should be able to take that same source and deinterlace it in the same fashion", but if I understand correctly, no, OBS would not be able to do that.
With a regular capture card, the process would go like this:
720x480 source (typical composite/svideo overscan)->Capture Device->480i framebuffer presented to OBS->OBS deinterlaces
But with the Elgato it goes something like this:
Case 1 (Elgato software):
720x480 source->Elgato->480i framebuffer to Elgato software->Elgato software deinterlaces and upscales to 720p
Case 2 (Elgato to OBS):
720x480 source->Elgato->480i framebuffer to Elgato drivers->Elgato drivers upscale to 720p, presents to OBS->OBS is unable to deinterlace this, because the scanlines are no longer intact.
If they can add support for keeping the input signal in its original format, it would work. However, with a PlayStation 2 game, you wouldn't really want to use retro/scandoubling to begin with, you want to use either field discard or the upcoming blend deinterlacing. Retro/scandoubling is intended for low resolution games and consoles, and most games on the PS2 are not low resolution ones.