Eterna Vivid were higher contrast stocks and rather grainy, so I'd be careful with pushing. I'd guess it might be usable with a push-1 and a preflash at EI800.
You can process a test strip with push-1 and plot a H&D curve to see how much latitude is there. I won't attempt push-2. Or better yet take a meter of film, shoot an over-underexposure test with a stills camera, push process, and try to print or scan it.
These were beautiful stocks (Vivid 160T my favourite of all films), but not the best for pushing. If you need an EI in excess of 1000, pretty much the only way to go is Kodak '19 pushed 2 stops.
Expired 8570, which's old F series, will likely show a lot of fog normally processed, even worse pushed.
Kodak '13 pushed 2 stops might be a usable EI640 film. You can even try a push-3 with that film - it's low con, fine-grained, and has insane latitude.