No. Ballet does not currently support deposits on the Base/Cronos/Optimism network.
When receiving crypto in the Ballet Crypto app, always use the exact asset and network shown for the receiving address. For example, if the app shows an Ethereum/ERC20 receiving address, do not use Base unless Base is specifically shown as a supported network for that asset in the app.
If you send crypto to a Ballet address through Base or another unsupported network, the transaction may be confirmed on the blockchain but not appear in the Ballet app. Ballet cannot cancel, reverse, or manually move a blockchain transaction for you.
For possible wallet-owner recovery options after an unsupported-network deposit, see the FAQ: How can I export assets sent to a Ballet address on an unsupported network?