I want to run BES but do not want to move from my current voice + text messaging plan to a BB plan. Can I run BES (I will be the admin) within my organization without a BB plan?

You must have a Blackberry Enterprise data plan. Some carriers only offer one option for the BlackBerry data plan, while others have it broken down to consumer and enterprise. If you don't have the enterprise plan then you wont be able to get BES email.

No. You need the enterprise BB data plan. The unlimited plans (at least in the United States) are highly recommended. Maybe you can get your employer to cover the data charges? (just a suggestion).

Your carrier doesn't offer an add-on Blackberry data plan? With an dd-on data plan you keep whatever voice plan you already have.