This is in the same vein as "Move, and you're a dead man," which is effectively a little roundabout way of saying "Don't move". A similar construction works in Japanese, too, but with みろ/ごらん:
Move an inch, and I'll shoot you.
Here (-て)みる is a subsidiary verb which basically means "to try something and see what happens." See: What is the difference between "verb＋て＋みる" and "verb＋(よ)う+とする"?
Likewise, in your sentence, ごらん is superficially a request, but the speaker is presenting something that must not happen using this ごらん. みろ/ごらん followed by a bad outcome is a common pattern.
こんなとこ三枝社長に見つかってみろ。速攻首だよ。(plain form equivalent)
Think, if President Saegusa finds me here like this? I'd be fired immediately!
Related: Is 「うそおっしゃい」 to be taken literally here?
(BTW this type of slangy そっこう "immediately" tends to be written as 速攻, although a few dictionaries seem to be starting to say 即行 is also okay.)