For sure someone can Douglas
First of all, dataconnections via mobile internet connections are as safe as they are if done with a normal PC with internet connection.
By default, you won't have the ability to make JDBC connections. There is no API for this build in Android.
What you can do is writing an Android App which will connect to a certain host via SSL connection (to gain security) and then collect data via some sort of webservice for example. This would in fact presume, that you have a server-side application wich will take your request, processes it, gain the required information from the server-side database and delivers the queryed information back to your Android device. Here you can do everything with these data, store them in a database or file .. whatever you like to do.
Summed up you will need some sort of client server application. One part running at your host the other on the Android device.
No matter how you do this .. security depends on the implementation of both parts. Server and client!
It's just up to you, how you retrieve and deliver the data
Hope my answer was helpfull for you even if my english is not that good.
lg Voss - Ach ja und noch was, die AndroidPIT-Regeln ლ(╹◡╹ლ) Android Security