Yes! Once you've chosen a template, click the Voiceover panel. Select "Browse for upload" and you can upload your pre-recorded voice-over or your own jingle right there. It will even work in the preview links.
You can adjust the voice-over/jingle and background volume by dragging the blue bars OR if the voice-over/jingle already has background audio, you can completely mute the template audio.
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The official file types we accept for voiceover upload are:
.mp3
.m4a
.wav
.aif
.aiff
.ogg