I don't think so. You are unable to link your account to steam. I tried to link my new account (bought ESO gold from the website for $30, steam was $60) to steam to use a gift card and it wouldn't allow me to. Everything I found on Google said the accounts can't be linked either. You can't just download the game through steam for some reason, you have to buy the base game through steam.
If you have purchased The Elder Scrolls Online on Steam and want to link your Steam account to your ESO account, follow the process below:
1.Open Steam and navigate to your Library.
2.Launch The Elder Scrolls Online from your Steam Library list.1.If not yet installed, you should click the Install button and allow the process to complete, then click Play.
3.Allow the ESO Launcher to completely patch and select Play.
4.From the in-game login screen, select the “I have an existing PC/Mac Elder Scrolls Online account” checkbox.
5.Input your ESO UserID and password and select Login.
6.Select Accept on the link confirmation window.
Your Steam account will now be linked with your ESO account! You can now log into the game and play by simply launching the game from your Steam Library.
Note: If your version of The Elder Scrolls Online was not purchased through Steam, you will not be able to link your Steam account to your existing ESO account without purchasing a new copy of the game on the Steam platform first.
The Elder Scrolls Online: Tamriel Unlimited - ZeniMax Online Studios