Thanks, I hope it was able to help you a bit =)
As for your question, no you can't catch Throdamas in the Wild, only the "basic" six: Dragon, Roc, Gryphon, Unicorn, Puma and Cockatrice.
The only way to regularly get Wild Throdamas is to go to the Battlefield. If you capture the Center Flag point (the "Portal") for 10 hours, you get either a Throdama or a Symurgh. But as you may have noticed this point on the battlefield is highly contested all the time so it's not that easy to do.
There used to be the option to buy wild Throdamas from events, where you would collect certain things and hand them in at the Warlock shop that opened up for that event. However, if memory serves, the last few events didn't offer the option to buy Throdamas at all anymore.. But maybe they will come back some time, who knows :)