Halaala

If a woman is divorced three times, I heard she can do halala with a third person and then return to her first husband (after completing the iddah). I know that it is not permissible to make halala a condition in the wedding contract, but it is permissible for her to informally agree with the man (the mohallil) to make halala (by speaking to him), without formally specifying it as a condition in the contract and without announcing it publically? The intention of both parties would be to make halalah so that the lady is able to resume her life with her former husband and reunite her with her family.