Sorry missed your post.
Yes that will cause a midi look in live if you have monitoring enabled.
The way I do it it love is to have two tracks, one with the input set to the P12 and one with the output set to the P12.
So you record to the track with the input set and then drag the clip to the other track for playback.
The other way is to keep it as you have it and turn local off on the P12, this can lead to some other problems though.