Simply 'connecting' might not have a charge, but it would probably be even more helpful to identify the phone (so a check can be made on its capabilities) and the network (as different ones charge different amounts).
As a quick example, I have in the past used WAP access to read my e-mail (on a 3-5 year old Siemens phone on the Virgin Mobile network).
It used to cost me about 2p per connection (they charged some fee per kB of data). Later on, I switched to some other tariff on one of my SIMs/numbers and any connection costs me a fee (30p for the day). That would be fine if I wanted to check umpteen times a day, but previously I might check a few times for mail, once on the train into town, again while in town - maybe twice even, and then on train back.
So I may have spent 8p to 12p for all my needs (unless I needed to respond, often there was nothing important I needed to answer immediately). Now if I pick up the wrong phone, it would cost me a once only 30p but still 2x to 3x what I really wanted to spend. A "plus" for VM and a "minus" for (this, low-usage) customer. Result, I don't bother any more!
On VM and the Siemens phone this was called GPRS (general packet radio service) which sounds to be what you are using...