The phrase "albeit secretive" is correct and usable in written English.
It can be used to introduce a contrasting idea, indicating that something is true despite another characteristic, in this case, being secretive.
Example: "The organization was highly effective, albeit secretive in its operations."
Alternatives: "although secretive" or "even if secretive".
For many, the decision to indict him wasn't up to a secretive (albeit methodical) jury, but to the public at least, the part of the public we agreed with.
The atmosphere is late Soviet: forbidding, secretive, careful, albeit not generally lethal.
Casting directors are among the most powerful figures in TV and film, able to make or break careers, but their world remains a secretive one (albeit not quite as closed as the Faith Militant).
The diminished influence of the partnership has forced Goldman, albeit begrudgingly, to shed some of its secretive corporate personality, especially in recent years as its opaque business model has come under scrutiny in Washington.
Who is looking into the no bid contracts for Halliburton, a company that has figuratively raped our treasury as its former head, our secretive vice president, smiles away (albeit crookedly) like the cat who stole the cheese?
Even as top Democrats denounce Charles and David Koch's political "dark money" organizations, party operatives have built a secretive nonprofit network of their own — albeit a much smaller one — to advance liberal policies and win votes.
The sharp increase in the number of executions in the kingdom has alarmed human rights groups and shone a light, albeit a faint one, on the judicial practices of one of the most secretive societies in the world.
Some teams are secretive about their finances, so some of these numbers are estimates, albeit informed ones.
I suspect this episode, which is reminiscent of Martin Cline's premature, shoddy, and secretive attempt at gene therapy in the early 1980s (which Cline continued to defend, albeit unpersuasively, in Rep. Gore's 1982 House hearing).
