No.  A normal L visa will let you travel anywhere in the country with the exception of Tibet.

Just remeber, if you do not stay at a hotel while traveling domestically inside China, you must report your address to the local Police station nearest to where you are staying within 24 hours of arrival

Additionally, an "L" visa or any another form of visa may not gain one egress into parts of Xinjiang, depending upon whatever the current cycle of events out there may hold in store.  There is a special process in place to obtain travel permission for Tibet involving the PSB but these days, a positive response is far from assured.

Chengdu - Zhenghzou, however, no problem.