Whether or not there is room on the 3pi depends on the size of the RFID reader you decide to use. The 3pi expansion kit isn’t always necessary for a project, but it can give you more space, make your setup cleaner, and more reusable.
It looks like the RedBee and 3pi are not compatible for both communication and power reasons.
It does not look like TX and RX pins are directly exposed on the RedBee board. I found this forum thread discussing the problem, and possible workarounds.
According to the RedBee user’s guide, the RedBee has a regulator on it that accepts 6 to 12 V and expects to have at most 1 A available to it. This isn’t really compatible with the 3pi power systems because Vbat on the 3pi can vary from 3.5 to 6 V (depending on the battery chemistry you choose and how charged they are), and the 3pi’s boost regulator cannot deliver 1 A to peripherals. However, the RedBee manual says the reader will only draw 80mA when idle but does not say how much it draws while active, so, it might be possible to power it depending on how much current the RedBee draws while active. You could try powering the barrel jack on the RedBee with the 3pi’s VBOOST. For more details about how much power the various 3pi power systems can deliver look at the FAQ about adding peripherals to your 3pi.