Hi,
iMessages is not part of iCloud.
Nor is FaceTime, iTunes, the App Store, iBooks, Games Center.
Those apps are a bit like logging in here.
It might be the same ID and Password you use in those apps but they are not part of the iCloud services.
They are not in System Preferences > iCloud.
If you click the Mail option in the System Preferences > iCloud then the emails are on the server - the app just reads them and shows them to you.
iMessages is a completely different server. Once you have received them then they are deleted from the server (never to be retrieved again).
Then can be flagged to be sent to several devices but even if a second device has not received it yet the first device cannot access that info.
going back to iCloud. If the Contacts option is ticked and it is the first device then your Contacts List is copied to the cloud.
All devices using the ID and the Contacts sync option can see the Addresses.
You can see them here https://www.icloud.com/ in the Contacts section (as similar with Mail)
If you Unsync the Contacts option in the System Preferences > iCloud then you are sometimes asked if you want to keep a local copy.
If it is already in the cloud then there is no real point.
These are the options on the iCloud web site after you login.

You can check them first if you wish.
iMessages once delivered are kept on your Mac in ~/Library/Messages in three databases.
If you also Save on Close all (types) of messages within the Messages app they are stored in ~/Library/Containers/com.apple.iChat/Data/Library/Messages/Archive
The "~/" bit is short for Hard Drive Name/Users/youraccountshortname
As Eric says make copies before hand if you are not sure.

9:31 pm Saturday; October 29, 2016
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)