No, it couldn't.
Russia fails to meet nearly all of the basic requirements for Commonwealth membership.
It lacks a historic constitutional association with either the UK or another Commonwealth member
It lacks any commitment to democracy and democratic processes, including free and fair elections and representative legislatures;
It doesn't adhere to the rule of law (neither domestic nor international)
It doesn't adhere to principles around international co-operation, use of force and coercion
It lacks an independent judiciary
It doesn't meet standards of good governance, including basic transparency of public accounts
It doesn't protect of human rights, including racial and religious discrimination
It doesn't have freedom of expression
Only to Russian propagandists