The Mexican angle would absolutely not increase the Handmaids' chance for liberation.
Currently, some women who come to the UK (say) from cultures where it is commonly believed that women should be chaperoned at all times by a family member/husband, are heavily controlled/monitored for the duration of their visit by a group of trusted persons. Say they've come here to study for a month, usually they are housed together, they are taken to/from destination with a nominated chaperone, in pre-arranged transport, have their time heavily organised etc. In some instances, courses are closed to other nationalities/religions/men, or the chaperone sits in if they are more open and so on.
So if Handmaids were taken to Mexico, they would be under the same threats/promises upon their return to "freedom" to ensure they 'completed the contract'. Aunts would go with them. Same ceremony, same coercion, same rules apply. Scenery is a bit different when they are permitted to be escorted out. 'Tis all.
They would not be able to "defect" because they would not have access to police/health/safe houses/charities/helplines etc. Nor would many be able to speak sufficient Spanish, obtain access to money/food/sympathisers and so on. There would be no asylum for them to apply for.
Also, they would be shared out amongst men who were trusted/connected to Mexican regime who arranged their repatriation. Those men would have no interest in liberating the women, quite the contrary. They would collude with Gilead to keep the women bidden.
They would be no closer to escape than now. In North Korea, defectors families are usually imprisoned even if they knew nothing of the defector's intention. But some NKs do visit Western Cultures...very few defect. Very few do because of fear for their families but usually because they will be rewarded on their return. If they do defect, however, we have asylum for them including access to money/housing/food and translators.
This is the reality now for people in regimes which subjugate women/human rights. But not so for the Handmaids if sent to Mexico.
So the Handmaids will be promised an elevated life/status upon their return to America post "contract", or death/colonies if they don't comply.
Being shipped to Mexico would make it much harder for them to escape. It would most definitely not increase their chances of liberation.