Yes, of course you can set the value to some variable.
Dictionaries are perfect for use together with local storage, because you can easily save and load a lot of information at once.
If you are saving each variable separately in LocalStorage, you need a million of events to save and retrieve each item. If you are saving a dictionary, you only need a couple of events.
I also suggest keeping dictionaries not just to store data in local storage, but actually using them in your game. For example, you can have a dictionary GameSettings, with keys like "MusicVolume", "SoundVolume", "Difficulty" etc.
You don't need to create variables with the same data, just use the dictionary, for example:
Audio set volume to GameSettings.Get("MusicVolume")