"despite having done" is correct and usable in written English.
You can use it to express the idea that something happened in spite of an action that had been taken. For example, "Despite having done my best to prepare, I still failed the test."
Du Pont always denied killing Dave Schultz, despite having done so in view of Dave's wife, Nancy.
Vanunu reports the German woman was harshly treated, including lengthy and aggressive questioning, despite having done nothing wrong.
Then we got to the Giro and Visentini is made leader despite having done nothing all season.
One of Galloway's campaign managers, Naweed Hussain, switched sides 10 days ago, despite having done the same job for Singh over three general elections.
One professor we spoke to described practitioners, casually but with some confidence, as people who earned "elephant salaries" despite having done less well at school.
Despite having done his homework, dressing the part, and trying to be a politician among politicians, he was still a 20-something among retirees.
In spite of my apprehension, however, I feel this could possibly be the best thing I could ever do, despite never having done anything like this in my life - is it as daunting as I think it may be?
SnapTerms has about 100 clients to date, despite not having done press or having advertised (save for once on Startups.com).
They are also overwhelming favourites to win gold in this summer's tournament, despite never having done so before, winning four silver medals and two bronze.
Though it's notable that PlaySquare has earned those eyeballs despite not having done any promotion for the app, it still has a way to go.
Failures despite your having done due diligence on investigating their condition and their prospects.
