In order to get your OTA, does your data or anything else need to be on or will it just happen as long as the phone is on?
I'd say keep it on. Even if you just keep it on 3G. You can always change it in settings>wifi/network>mobile network>select network>it will show LTE automatic and CDMA mode. Choose CDMA mode and choose either home or automatic. Doesnt matter which one but you'll be on the 3G network at all time and it won't search for 3G and all in all save a tiny bit of battery life. Again to your question as well; I think the update needs data to download so my guess is, keep it on. Hope this helps.
sent from my Droid Charge/SCH-I510