Im not sure which LG phone the P990 is unless its actually the LG 2x :P. But yes you can.
The trick is importing all the contacts from sthe sim to the phone. And then change the contact "setting" from Phone to Gmail/Google and then it all gets synched there.
Only downside is that all contacts that you have on Google that emails you and such, gets synched to the phone as well. So I regularly go through my google contacts and clean them out to remove all those contacts I dont want. Either that or simply choose not to show contacts without a phone number in my list of contacts on my phone.
Samsung Galaxy S3 4G