Hi,
You can export to PNG strips and GIFs freely and import these images anywhere (Godot, Unreal, etc).
It is not possible to dictate the exact path, only offsets and gravity (which makes them attract to a certain direction).
"Would it just be a matter of us needing to manually determine a speed and lifetime for the particle by hand to get that sort of effect?"
Yes, you would have to manually setup the lifetime in order to achieve necessary effect.
Thanks!