Havel would actually find some level of agreement with the idea that the election of the American Presidency can reflect the inner soul of the people.
The idea of free elections would be something that Havel could see in America that is a part of the "inner soul" of the people. Coming from a repressive Communist regime, Havel would be particularly mindful of how elections in America can represent popular sentiment. He would probably be encouraged by the limitations fostered by campaign finance reforms that seek to limit contributions to political campaigns. This helps to preserve the "inner soul" element in ensuring that the wealthy do not exert immediate control of the political process.
At the same time, I think that Havel would not entirely feel comfortable with other elements of the American electoral process in its desire to reflect "the inner soul" of the people. On one hand, the electoral college math would not necessarily reflect "the inner soul" of the people. In the most recent Presidential Election, a handful of "swing states" helped to determine the outcome. Both political campaigns understood this, heaping millions of dollars in these swing states in order to get their candidate to 270 electoral votes. This does not reflect "the inner soul of the people," and Havel might have a problem with a few states playing such a definitive role in a nation's leader. At the same time, the idea that the popular vote does not determine the President would be a major element that seeks to go against "the inner soul of the people." Conceivably, the President is not elected until the Electoral College votes him in, and these voters could go against the will of the people. While it is unlikely, it is possible, and Havel could see this as going against "the inner soul of the people."
Finally, one point that might suggest Havel would oppose such a notion is that the clear establishment of the two party system in American politics as the only viable option for the election of President does not entirely reflect "the inner soul of the people." Being sensitive to the silencing of voices, Havel might suggest that leaving the people with only two viable political options fails to account for the divergent and eclectic political nature that is within the inner soul of the people.