All I've found on Thea in the comics is this on Speedy who appears to be mostly unrelated besides name.
In Arrow though from what I've seen (up to S3E13) Thea is:
Trained by Malcolm Merlyn, whom both end up joining up with Arrow.
Does this have relation to Arrow's sister in the comics?
She is an amalgamation of multiple characters from the comics
Including Mia Dearden. The writers hint to this by making Dearden her middle name.
This blog post sums it up better than I could:
When Thea Queen was introduced, it immediately became clear to me that we would see the second version of Speedy, Mia Dearden. Further proof of this soon came when we learned that Thea's full name was Thea Dearden Queen. However, since then, we have seen her draw elements from various characters which include the likes of Cheshire, Mia Dearden, Artemis Crook (Young Justice Version), and Arrowette.
Thea Dearden Queen seems to be the Arrow version of Mia Dearden. Her popularity led to Green Arrow comics give comic Oliver a sister named Emiko Queen who uses the alias Red Arrow.
