Ranked MMR and normal MMR are definitely not synchronized.
You can see it when mostly any LoL pro (or anyone who improved in rankeds since last normal game) plays normals - they stomp hard, because their normal MMR is much lower than their more accurate assessment of their skill - their ranked MMR. If in such game their enemy team has ranked players, their ranks would reflect that unless they are in similar position (i.e. improved since last normal game) - their ranks would be much lower than that of said pro/high-elo player.
Kinda related: Solo queue MMR does not affect Team MMR in no way way; besides maybe placement matches.
There are ways to test this hypothesis in a way - see http://op.gg/ for soloq and ranked team MMR or if you don't trust it's algorithms, just find a team with ranking severely below individual rankings (due to lack of communication etc), which is pretty common in lower divisions (higher up discrepancy is a bit less, by my observations)
- followed high-elo/pro NA/EUW/KR scene for several years
- saw effects of this in action as described above
- was interested in MMR innerworkings myself
- currently can not find Riot's information regarding this but remember reading it
- some minimal research shows that it is common knowledge.