Yes; it would provide me and my elected representatives with tangible evidence of economic damage to point to in support of our case against the invasion.
I don't really think it works at all. If other domain services are available, its just annoying. If NONE are available because they all agree, its just deplatforming basically.
Do you think Namecheap would turn off Americans (their own country, regardless) domains as a method to get them to agree to call their reps and stop a war? I somehow doubt it.