The answer
For a standard Ethereum mainnet transfer, no: the account needs ETH for gas. Some sponsored or account-abstraction services can pay the fee on your behalf.
What to do next
Confirm whether your app explicitly offers a sponsored transaction. Otherwise obtain enough ETH on that same network to cover the fee.
MetaMask
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Ledger hardware wallet
Relevant hardware-backed signing for supported assets; it does not eliminate gas fees, contract vulnerabilities or approval risks.
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Frequently asked questions
Why does the token balance remain visible when the wallet cannot send it?
The token is owned on-chain, but a normal transaction still requires network fees.