If you're setting up personal email accounts separately from the BlackBerry server hosting your business email, no, your personal emails, call data, etc. are safe from the company. If you route your personal email to the company for use on the BlackBerry then yes they will have access to your personal email.
Something to consider, with your BlackBerry under their control they could deactivate and lock the whole thing at any moment which would render the unit inoperable until the situation is resolved. Depending on how the usage policy is worded it may be completely legal as well. They could also deploy applications and other settings that could be used to poach your data, but this is malicious and unexpected.
How much risk are you willing to endure for the convenience of business email, and how important is your personal data if it was compromised?