Neither AES-NI nor ChaPoly can be influenced by this vulnerability, because they do not use the secret key with different kinds of instructions, that might consume different powers. The secret key is used only in XOR operations. Other secret state of the ciphers is also used only in simple operations, e.g. XOR, additions and rotations, where there is very little variation of the power consumption depending on the operand values.
The cryptographic algorithms that have chances to be influenced are those based on public keys, which compute arithmetic operations with large numbers that can cause changes in the clock frequency.