Is there a way to search for a number in Google while keeping the ongoing call intact? I have noticed that the internet connection is lost when a call is in progress.
I believe this depends on your provider.
For example: Verizon's CDMA network does not allow you to do Data + Call; however AT&T's GSM network will.
And as eldarerathis points out:
Another potentially important distinction is that phones on CDMA carriers with other networking capabilities (WiMAX and LTE) will support simultaneous voice and data since they're essentially operating on two separate chips, so this can also be dependent on your device.
So this ends up being device, and carrier dependent.