BwPostman is tested on many Joomla!® installations without problems. Most notably I test with the current Version of Joomla!®, partly also with the preceding version. Nevertheless I can't exclude that something goes wrong during installation. Especially the „interplay“ of different extensions can't be estimated fully and negative effects can't be excluded.
I suggest to always backup the complete system (database and files) before you make changes to your Joomla!® installation (installation or update of an extension)! For this task the free version of Akeeba Backup e.g. is suitable.
Since BwPostman 1.0.1 the possibility exists at maintenance to save and restore the tables of BwPostman directly from BwPostman. Furthermore since this version there will be created a backup file of the tables of BwPostman at each update and the tables were checked on consistency. Particulars in chapter Update.
Testing an unknown extension – this is also true for BwPostman – it is highly advised not to do at a life-system.