Yes you can put Drano in your garbage disposal and it will do no harm to the Garbage disposal as long as you follow the instructions on the bottle of Drano.
I've used Drano in my Garbage disposal and worked just fine and never harmed the garbage disposal.
You can use any type of the Drano in your garbage disposal but the best Drano type to use for clearing clogs in garbage disposals is the Drano Max Gel Clog Remover.
Put the Drano Max Gel Clog Remover in the garbage disposal and allow it to sit for 30 minutes to an hour to clear the clog.
Larger clogs may need the Drano to sit longer.
Then you can pour boiling hot water down the drain to help clear the clog and flush out the Drano.