How effective was the strategic hamlet program initiated by the Americans effective at limiting support for the insurgency?
The strategic hamlet program was not at all effective in limiting support for the insurgency. In fact, it may well have increased that support. This is largely due to the fact that the program was so closely tied to the unpopular Diem regime and was largely run by that regime at its own pace and for its own purposes. However, there is no way to prove that it would have worked even if it had played out exactly how the US wanted.
The program may well have been doomed from the start. It was extremely unpopular among the rural population. They did not like being taken away from their lands and their homes and being forced to live in the strategic hamlets.
This initial problem was made worse by the way in which Diem ran the program. From the American perspective, Diem's goal for the program was to impose his control over the populations of the strategic hamlets. This ran counter to US desires to win the hearts and minds of the population. Diem's actions helped to make the program even less popular than it might otherwise have been.
The whole purpose of the program was to reduce support (both economic and in terms of opinion) for the insurgency. However, the program annoyed and alienated the people whose support it was supposed to win. For this reason, we cannot say that it was at all effective.