Hi,
It depends on how the payment plugin is developped.
Some payment plugins will directly output the debug information to the customer and in that case, you don't want to keep that turned on outside tests.
Also, the debug data can contain sensitive data about your merchant account that will be stored in the log file. If the log file is compromised by a hack in the future, the attacker could get a hold of your sensitive information. So if you don't need to do debugging, it's best to keep if turned off. That will also save some space as the log can be quite big if you have a lot of transactions.
But if you don't care about both of these points and that the plugin doesn't directly output anything to the customer, then you can indeed keep the debug turned on.