In short, no. To get an accurate location you need a mobile device with built-in GPS.
The Cell ID is a number identifying the cellphone tower that the mobile device is connected to. Therefore at best you can get the position of the cellphone tower, and use that as an estimate of the user position.
Also note that API's such as http://www.opencellid.org/api only give an estimate of the cell tower position based on data from other users, so it might not even be an accurate position for the cell tower.
In my experience this will work reasonably well in densely populated cities - you can get an accuracy of about 200-500m (still not close to what you'd get with a GPS). However, in more rural areas the accuracy could be as low as 10 or 20 km.
As pointed out by Baba, triangulation can give you a more accurate position. However, for this you need the distances to at least 3 towers, while in J2ME you can only get the ID of the closest tower (not even the distance). Some network operators do triangulation themselves, as they have all the data available to them. However, you'll have to talk to the specific network operators if you want access to this data.