That all depends on whether or not you are a captive agent or a broker ( of course depending on which test you took), If you are a captive agent, meaning you work directly for an Insurance provider and sell and are allowed to only sell the products they provide you, I would be hard pressed to believe you can just walk out with your book. In that case you can solicit your BOB to another agency within the company and believe that even then you will have to have the consent to sell from corporate.
Now, if you are a broker meaning you work in an insurance office which provides services from various carriers and you procured your clients of your own accord and ( and here is the catch), you rent your space that you use in that office (inclusive of utilities), you can indeed walk out with your book, no harm no foul.
If you are working for a GA (General Agency, or you were hired by the office where you work) then it is implied that the work afforded to you was supplied by the owner(s) of that office and therefore you are not entitled to leave with anything out of that office but your hat.
On a lighter side, I faced the same dilemma once, and left everything behind, turned out that I became that much more determined to become a success and so far so good. If you have a chance to grow take it!