There IS a battery in the MagicBands. If you want you can
read the FCC filings 
It's non-replaceable as it is encased in the plastic with the chips and antenna.
The MagicBands will contain two RFID chips (one for HF and one for UHF - not exactly sure why they need two), PLUS an RF transmitter working at the 2.4GHz band (same as Wi-Fi) that permits reception at a longer range than the RFID chips (at best they are read at 1-2m in normal circumstances, much shorter is more typical). This is the part that Iger's Markey response refers to when saying that those who opt for RFID cards may not get to experience all the features, as they won't have the transmitter or battery. I believe somewhere in Iger's response it also mentions the transmitter.
Although the 2.4GHz band is typically effective to 300 feet outdoors, if they are using a lower power output (and these will only put out a fraction of a watt, much less than a cell phone), the range will be lower and the battery should last well enough. I'm hearing the effective range is 10-15 feet.
This transmitter is believed to trigger some of the new "experiences", like personalized items on attractions and information for the characters for the meet and greets, so it won't require having to explicitly scan their MagicBands. And it's part of what has people concerned.