If my iphone is backed up to icloud, would it matter if itunes was to delete everything on iphone?

I rececntly got a new laptop and, when trying to put some music from it to my iPhone, it wouldn't let me. This is when I discovered that I needed to click the button that says 'manually manage music and videos' However, when I went to do this, it said "An iPhone can be synced with only one iTunes library at a time.Erasing and syncing replaces the contents of this iPhone with the content of this iTunes library."

I have backed up my iPhone in the cloud so, would this be enough so that I could apply these settings and then get my data from the iCloud and transfer it over? If so, how would I do this?