No. Cashu is only for total new users that start from 0.
Having already channel is perfect, only be sure you have enough inbound liquidity.

For a small private node like that I suggest to have 2 channels:

• one with more outbound liquidity, to be able to make payments
• one with more inbound liquidity (you can buy an empth one from LSP) to be able to receive easy and more payments.

Once one of the channels is depleted/full, just swap out/in accordingly.