Why is GPS almost unavailable without data connection?

In theory, yes.

However, you must be aware of a few things:

1) GPS does not work well on high latitude (GLONASS is better in this case)

2) When you change location, the GPS needs to get information about the position of the satellites (so called almanach) for efficient use.

3) in cities, especially with tall buildings, the satellites are "hidden" by the buildings. Therefore you may not have enough "visible" satellites (4 are necessary) to compute a position.

4) The GPS satellites are moving and you don't have the same number all the time. Usually in open areas you always have enough satellites, but as I said you need more chance in "closed" areas. There are softwares to know the best moments (based on the almanach, the location and the field of view)

5) Eventually, I don't think that Galaxy Nexus has a good GPS sensor. The price of a GPS may range from 100 to 20000 $ and this obviously leads to a large difference in terms of correction for multiple travels (signal bouncing on a building), precision (15 m to a few cm...). You use a phone for locating yourself, with a GPS add on. The phone based location (using GSM towers) is therefore far better than what you get with GPS signal.

The Faster GPS tool depends on network connectivity.

So you will have no luck in using GPS without a connection. If possible, disable it to get offline GPS reception. That is, connect to the satellites (for free), and not to the mobile cell transmitters (for payment).

Or use a GPS receiver without mobile connections.

To get a first fix, select a place open to the sky, and wait there without moving, until you have a fix.