No, VoLTE support is not really limited by LTE bands.
For 4G handsets, VoLTE is mostly limited by the whitelist in the handset software. If your PLMN is not in the whitelist of the handset, then VoLTE capable handset attached to 4G on your network will still refuse to use VoLTE with your network. And make no mistake, the whitelist is short.
However, it does seem that there is hope with Apple. With updated iOS and iPhone 7 and higher, the user can actually enable VoLTE in the settings - even if the PLMN of the network is not in the handset whitelist.