Yes I know DocuSign well and this is absolutely possible. You are right in that you want to use Embedding, with Embedding you can generate URL tokens to access envelopes as a sender or recipient, and you can also use it to access the DocuSign Console.
The following two resources have all the info you need including working examples of Embedded functionality in 6 different languages. I'd start by reading about them on the DocuSign Developer Center in the Explore -> Features section
Then they have their API Walkthroughs which are EXTREMELY valuable for Embedding and other use cases. Check out the bottom three 3 squares for Embedding