Erleidet einer meiner Leute Schaden, werde ich ...
I wonder if this amounts to saying:
Wenn einer meiner Leute Schaden erleidet, werde ich ...
If so, is this omission of wenn commonly seen?
Yes, this is indeed an unmarked conditional clause, i.e. wenn or falls (to indicate conditionality) are missing.
These clauses are actually really interesting because they are one of the few examples in which the finite verb occupies first position — as in a question. Grammatically, they are actually main clauses due to the lack of a subordinating conjunction (wenn/falls) which is also why the verb needs to shift in final position if you add wenn in your example.
The construction is fairly common, but in my humble opinion marked conditional clauses are much more frequent.