GSM, CDMA, WCDMA and LTE are all mobile network connections used for acquiring aGPS data.
So if your device has a standalone or hybrid GPS as well, you can use GPS without any problems (meaning as long as there is satellite reception). With aGPS your time-to-first-fix (TTFF) is much quicker, especially if its been awhile since last using GPS.
So to answer your "IOW", yes you will lock onto signal very fast if mobile data is enabled, as opposed to disabled.
As to: " Does it mean that it will never use A-GPS to download data from the Net even when a data connection is available through GSM ? ". No, it will use available mobile network connection for acquisition of needed data.
Take a look at this, since you said travelling around your country (could help if accuracy becomes an issue)
Standalone GPS units depend only on radio from satellites. A-GPS does that as well as using cell tower data to enhance quality and precision when there is poor satellite signal conditions. A GPS unit may require as long as 12.5 minutes (the time needed to download the data - GPS almanac and ephimerides) to resolve the problem and be able to provide a correct location.
To be more precise, "A-GPS" features are mostly dependent on an internet network and/or connection to an ISP. A mobile device featured with "A-GPS" (no additional GPS feature to be selected as alternative) can work only when there is an internet link/connection to an ISP.
For a little more info look at aGPS Wiki