Bad things. Very bad things.
Seriously though, there is a way to do it, but it is more involved and there are guides on how to go from ZVD to ZVH and back on this forum, if you want to try that at some point. ZVD is the current stable release where everything still works; ZVH is newer but Sprint/LG botched it and it has a bunch of bugs.
Here's my crude understanding of radios (i.e. ZVD/ZVH): It's firmware that only the stock recovery can/should manipulate. Installing a new ROM does not effect the radio, but different ROMs are dependent on specific radios to function. If you have a mismatch, a bunch of your apps may not work properly and you will not have a data connection, if it boots. Moral of the fable: Don't mismatch. Only install ROMs that are designed for your radio/baseband.