On retirement from the company, an employee, be he a secretary or CEO, is presented with a gift pack containing a selection of its products.

原句被动语态漏掉了be.

be he a secretary or CEO 为whether引导的让步从句省略了whether。

be he a secretary or CEO 古体，非常正式

= whether he be a secredary or CEO 古体，非诚正式

= whether he may be a secretary or CEO 现代英语正式语体

= whether he is a secretary or CEO 现代英语普通用法。

be+主语+其它属于古体倒装虚拟语气结构，可以理解为相当于是省略了whether...or ....结构，无论A还是B

Whether 主语+be A or B

Whether 主语+ may be A or B

Whether 主语 is A or B

be he a secetary or CEO可以用下面几种结构替换

(1)whether he be a secetary or CEO

(2)whether he may be a secetary or CEO

(3)whether he is a secetary or CEO