This really is not good enough. If people see things that way then they are misinformed. The have been misinformed by the representatives of the bosses. That is to say the media and most politicians giving a constant drip of propaganda intended to undermine the union movement.
If you want the union to be effective you must educate the misinformed members.
And I have remembered something having read Guineveretwo's voice of experience. The GMB is debarred from recruiting from another union while that union is involved in industrial action, by something called the Bridlington Agreement.
There would be no cover that an unrecognised trade union can give members apart from last resort legal support at a tribunal. - if the union chose to do so. There would be no point in being a rep because you or anyone else will not be permitted to represent their views to management. You would be able to act as a 'friend' and be in attendance at a redundancy appeal but this would be little more than a token. The PCS members would get a better deal in this circumstance.