No, Ethfinex wallets are only designed for trading and funding purposes. They are not developed, nor are they intended to replace local wallets. Local wallets are suited for broadcasting transactions for general purpose use, including making purchases. If you intend to make routine payments or time-sensitive transactions, you must use a local wallet.
Ethfinex wallets are not designed for long-term storage. Local wallets are designed for this use-case and will serve such needs best. Ethfinex wallets are designed for high activity, frequent usage, and routine trading, not storage.