Short answer: Of two trained Jedi, if at least one was a member of a naturally-occurring telepathic species, then it may be possible for the two of them to be on opposite sides of a planet and be able to communicate, at least in a limited fashion using the Force.
If we assume two skilled Force users, then the power called Force Telepathy allows communication over vast distances depending on skill, power level, and innate telepathic ability. Even untrained users could experience telepathic connection if they were related, for instance. Luke and Leia were able to connect briefly even when Luke was just a padawan trainer.
The more complicated answer:
The terms "Force sensitive" and "Force user" are not synonymous. A sentient can be "Force sensitive" and not be a "Force user". All trained Jedi are Force users. An untrained padawan is most likely "Force sensitive" and that is why they were selected for training.
The term "Force sensitive" was used to describe sentients who were untrained in the ways of the Force. They were able to use it naturally to alter their probabilities of success, having a knack for certain skills such as flying or podracing, feats of speed or strength, or even to unconsciously manipulate the Force directly, with very sporadic results. This use of the Force by a Force sensitive person was considered unreliable (but detectable, if you knew where to look). It is safe then to assume, that the untrained "Force sensitive" will not likely be able to use Force Telepathy to communicate reliably with anyone other than a highly trained Jedi.
So if I refine the question: Can two trained Jedi who are on opposite sides of a planet still communicate via the Force even if their radios or other communications are offline?
Possibly, since one of the powers able to be granted or augmented by the Force is telepathy. But the telepathic ability granted by users of the Force if their species is NOT naturally telepathic is very limited. Only two people who shared a strong bond, such as family members, master and apprentice, or lovers would be able to utilize such a telepathic link and depending on the relationship, there may be limitations on what information could be shared, how long a message could be or how much detail could be shared. Most likely such a link would have a relatively limited range (Wookieepedia's article on Force Telepathy indicates a distance of a thousand miles or so.)
However, a Force user whose species was already telepathic could experience a boost of a thousand times greater range, effectiveness and clarity to their already existing natural telepathy. This would allow distances capable of encompassing an entire planet and in the case of powerful telepaths, potentially star-systems.