Sure!
You can create animations yourself and export them as videofiles (*.mov) DXV codec to load and play on Resolume.
Or
You can just load your logo jpeg image (better PNG with transparency) and apply some moving attributes and/or effects within Resolume. You can even set them to interact with your audio.
You´d better load a still image of your logo as a video file than actually importing a PNG due to memory usage.
The kind of movement you will find using Resolume internal tools are mostly like rotate, stretch, scale, zoom in/out, some tile and/or cubic arrays.
There are no ready loops for logos. If you can´t find any music, try enabling external audio input. You can use your mic to "listen" to external audio and music being played.
Clips, attributes, FX, they can all be affected by audio. Check the manual or tutorials online.
I have a composition for this same purpose. The logo is on the bottom layer and the effects are on the layer above. You can drag effects on to empty spots on your effects layer. This allows you to trigger them on the fly or use autopilot to make them switch automagically. Let me know if you need further explanation.