Cloudlifter CL-Zi with a Shure Beta 58A: the three-position switch is attenuation, not three levels of gain
Yes. With the Cloudlifter CL-Zi already in line, the Volt 176 only has to supply about 26 dB of the 55 it publishes. Those are the published figures.
The hard gain is already done. The Cloud Microphones Cloudlifter CL-Zi sits in front of the Universal Audio Volt 176, so the interface preamp is no longer the thing that has to rescue a quiet microphone.
Shure rates the Beta 58A at -51.0 dBV/Pa, the voltage from a loud 94 dB tone at the grille. A speaking voice is closer to 85 dB, so the preamp still has to find about 26 dB to land near −9 dBV. That −9 dBV figure is just a tracking level: high enough to use, with space before the converter clips.
Feed the interface from the booster's output and do not stack a second microphone preamp on top. Most inline boosters spend the 48 V themselves. That is fine for a dynamic. If this microphone is a condenser, read the booster's manual before you leave it in the chain: if it does not pass phantom, the capsule goes silent.