Q: Is it safe to sync contacts with google contacts ? The wheel in contacts is spinning

Safe is relative.   Never work on the only copy of something if you have never tried working with the solution before.

It is best to backup first to a local hard drive, flash drive, CD, DVD, computer, and then try over the net.

The net is a good backup if you want something that will survive theft or accident in the home, or damage to equipment at home.

See my tip on backing up.*  http://www.macmaps.com/backup.html

What you can do, is copy your contacts file on Users -> yourname -> Library -> Application Support -> Addressbook folder to your desktop.

That will allow you then to back it up elsewhere.   Do not move it, to copy it hold the Option key as you drag the folder and make sure the green circle is next to your pointer with the white plus.

At least it will copy the present condition of your Addressbook file in event something is wrong with the Google copy.  Since network syncing can take time, I'd leave it on overnight.

Only then would I start to worry.  It is unwise to stop a sync in the middle of the copying as then you might lose both copies.

* Links to my pages may give me compensation.