If you state something that cannot be disproven, your opponent has no way of countering you and so you are basically cheating in debate, especially if your unfalsifiable statement is highly improbable. Besides, unfalsifiable statements cannot be scientifically tested, so there is no definitive way of knowing the real truth about them.
If the fact is used in context and is valid to the argument, then it would not be cheating. However, it must be directly relevant to the subject at hand and have a clear and definite point. Otherwise, one is simply spouting useless facts to throw off the opponent. If the fact is used in all the correct ways and is entirely valid, then the one who has that solid fact may easily win the argument by being better with hard and undeniable facts. It may seem shady and underhanded, but if there is a hard fact used in and argument, that person is far more likely to win unless the opponent has a counter-fact to oppose it.
Showing that a statement cannot be dis-proven can be strong support for the idea. However, it can be countered be showing that it is very unlikely to be true.
Statements that cannot be dis-proven, and statements that something is unlikely are both forms of "inductive reasoning" which relies on strong support, as opposed to "deductive reasoning", which uses definite support (in the form of valid evidence and sound logic).
Inductive reasoning is a common tool in debates, but it is not the ultimate defense, and is no substitute for actual proof.