Yes. BlueMail supports BCC (Blind Carbon Copy) in full, and gives you three ways to use it depending on how often you need it.
Adding BCC to One Email
Compose opens with the To field alone, keeping the screen clear for the message most people are writing. Tap Add Cc/Bcc and the Cc and Bcc fields appear below it, ready for recipients.
Keeping the Fields Open
If you use BCC often, have BlueMail show the fields every time. Go to Settings | Accounts | [select the account] and turn on Always show CC/BCC in Compose. It is set per account, so a work address can open with the fields showing while a personal one stays simple.
The fields also open on their own whenever a message already needs them, such as a reply that carries Cc recipients.
BCC on Every Email Automatically
To keep a copy of everything you send at another address, BlueMail can add a BCC recipient for you on every message, with nothing to remember at send time. See add yourself or another email address to BCC automatically. Setting one is enough to make the Cc/Bcc fields visible in Compose as well, so you can always see what is being added.