Of course. They do now (work side-byside,) and do not interfere with each other.
DC extension code acts upon only components (instances and definitions) and group instances that specifically have an attached attribute dictionary named "dynamic_attributes".
Live Components have their own specifically named attribute dictionary.
So, “never the twain shall meet”. 
The Dynamic Components extension has not had any new features for many many years, and will (most likely) not get any more. SketchUp team has said this before. There are too many extensions (some Trimble) that now rely upon the DCs to remain as they are.
It has also been like “pulling teeth” to get errors in the Dynamic Components extension fixed. I do hope (and politic) for all existing easily fixed errors in DC code to be fixed, before it is “retired” to an optional extension.
So, it is most likely [speculating] that the Dynamic Components extension would be “frozen” at some version, and thereafter remain as such in the Extension Warehouse as an optional extension. (Ie, it may no longer be distributed as a “default” extension with the SketchUp installer. But [speculating] this is not likely to happen for several major cycles until after Live Components is mature enough.)
We are hoping that a conversion utility will be fielded that would make adoption “less painful”.
The LC interface allows much better and a larger set of controls for the end users (sliders, etc.)