UPDATE! Yes, it does! After the launch of Ledger Live, Ledger added support for TRON as well.
Earlier, before the mainnet launch, TRON (TRX) was introduced as an ERC-20 token which can be sent to an Ethereum address and managed using applications like MyEtherWallet.
Post mainnet launch, TRON has a different chain and Ledger has completed working on its support for Ledger hardware wallets. You can see the results here: https://trello.com/c/vXoV4l5I/104-tron-support