Yes, the whole time
Once you press 1 and we dial the destination, both legs are bridged into one normal, two-way call. You hear them, they hear you, for as long as the call lasts — nothing about the caller ID we display changes how the audio works.
Why this even comes up
A Spoofey call is really two separate phone calls joined together: one leg rings you, the other rings the destination. Some people assume that because it's two legs, only one direction might be routed — that's not how it works. Once the bridge is up, it behaves exactly like a normal three-way call would, minus the third party.
If you only heard one side on a specific call, that almost always means the call never actually bridged — check whether it was cancelled at the press-1 step instead.
Under the hood
Both legs are ordinary SIP calls to your carrier and to the destination's carrier. If you're curious how that protocol actually works, we wrote a plain-English explainer on SIP.