You cannot import a JAR implementing java.*
classes easily. And, JDBC would need to be ported to Android, since it probably relies upon classes in JavaSE that Android lacks. And, you would need to write your own JDBC driver for SQLite anyway, wrapping the API Android already supplies, since I suspect the existing JDBC driver uses JNI. And, when all of that is done, you will have an application that adds a lot of bloat, making it less likely people will download and retain your application.
In short, I wouldn't go this route.
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