Pretty close, but the local bodies (Local Spiritual Assemblies) do not directly elect the National Spiritual Assembly. Rather, local communities elect one, two or sometimes three delegates, according to the number of Bahais in the area, and the delegates go to a national convention, where stuff is discussed and the National Spiritual Assembly is elected.
However, all the members of the National Spiritual Assemblies are delegates to the international convention, which at present is held every five years.
Because there is no campaigning and no candidates, the incumbent members are almost always re-elected. Turnover is largely a matter of sitting members who indicate they cannot continue. But there are times when a national community gets seriously pissed off: in one case six incumbents were not re-elected, and the incoming National Assembly sanctioned one of the three who were re-elected (for misapplication of funds), so that NSA ended up with seven new members. When a member cannot continue serving, or when the delegates are so annoyed with the NSA that most of them decide not to vote for the incumbents, the selection of replacements is almost random, since the pool of people who could be elected is very wide. (This is why it takes major dissatisfaction to cause an electoral upset).
Having said that, there are times when an individual emerges who is so evidently capable that he or she gets elected, even over one of the incumbents. But it's rare.
This is rather different to the logic of civil elections, or even elections to the board of a civil society organisation. The focus is not on obtaining the highest quality of members, but rather on the potential of members -- any members -- to achieve good decisions by consulting together. In fact, before the voting system was introduced, Baha'u'llah provided a decision-making method that started with drawing nine names out of a hat (or turban?). His faith really lay in the combination of consultation and reason, rather than in finding outstanding individuals.
It's rather different in the case of the election of the Universal House of Justice, because in 1973 (if memory serves me, but it's hard to get decent help these days) the UHJ established a new institution at the World Centre, the International Teaching Centre. This has come to be a pool of candidates for the UHJ, in effect. All of the present members of the UHJ were members of the ITC when they were elected. This is seriously bad stuff for the Bahai Administration, because the UHJ sits at the top of the 3-layer pyramid of elected institutions, and its members logically and practically should be drawn from those with long experience on National Spiritual Assemblies around the world. Instead, the UHJ appoints Councillors (members) to the ITC, who are suited to the work of the ITC and who usually have prior experience as continental councillors -- and then the delegates to the international convention take these people, who were doing the work the UHJ thought they were best at (which does not include administering Bahai communities), and moves them onto the UHJ, which has a different kind of work to do. The UHJ as a result has no members with long experience on an NSA, and every time this happens it has to fill the gaps in the ITC.
This is fixable, either by abolishing the International Teaching Centre (it is not mentioned in scripture, so it can be changed or abolished), or more probably, by the UHJ stating that the Councillors it has chosen to work in the ITC should be allowed to stay there. The UHJ, or the Councillors, would have to suggest to the convention delegates not to elect sitting Councillors to the Universal House of Justice. There are good precedents for such a request. The first is the example of the Hands of the Cause, who by asking the members of the National Spiritual Assemblies not to vote for them (Ministry of the Custodians, p. 20) gave concrete expression to the separation of the spheres of authority and administration on the one hand, and of guidance and wisdom on the other hand. There was a similar policy in the time of Shoghi Effendi. His secretary wrote "… the Guardian states that the Hands of the Cause are eligible to administrative offices except those permanently residing in Haifa and helping the Guardian in the administrative work. (Letter of May 30, 1952, on behalf of Shoghi Effendi, published in The Light of Divine Guidance v I, p. 182)
In the present-day structure, membership of the UHJ is an "administrative office" and the ITC is the descendant of the group of Hands of the Cause who one lived in Haifa to help Shoghi Effendi. So it's no great stretch to use the 1952 letter as precedent for saying the ITC Councillors are not eligible for administrative offices. Perhaps the UHJ is already moving towards declaring the Councillors non-electable, as at the continental level it has stated:
"...the Universal House of Justice has decided that Counsellors, during their terms of office, are not “eligible for membership on national or local administrative bodies… ” (Wellspring of Guidance, pp. 141-142) and it has asked the members of the Auxiliary Boards to suggest to delegates at national convention, that it would not be desirable to elect them to the National Spiritual Assembly: National Assemblies in whose areas of jurisdiction Board Members reside, should point out to the delegates at Convention that whilst teaching and administrative duties are not mutually exclusive, it is desirable that Auxiliary Board Members, whether for teaching or protection, be left free to concentrate on the work allotted to them… "
The same surely is true of the members of the ITC: they should be left to concentrate on the work allotted to them. However the freedom of the delegates or electors to vote for whomever they wish is a great good: note that the language in the last letter I quoted only suggests what is desirable, without laying down a rule. In the Guardian's time, however, the 9 "Hands of the Cause" were simply ineligible.
