A good number of the Hands of the Cause were still members of National Spiritual Assemblies at the time of the Guardian's death. For example, see "UNANIMOUS PROCLAMATION OF THE 27 HANDS OF THE CAUSE OF GOD" at http://bahai-library.com/uhj_ministry_c ... apter=1#28
where many of the undersigned are listed as being National Spiritual Assembly members or officers.
In 1964, however, the Universal House of Justice did declare that the Hands of the Cause were ineligible for election or appointment to administrative institutions:
"The exalted rank and specific functions of the Hands of the Cause of God make it inappropriate for them to be elected or appointed to administrative institutions, or to be elected as delegates to national conventions. Furthermore, it is their desire and the desire of the House of Justice that they be free to devote their entire energies to the vitally important duties conferred upon them in the Holy Writings...."
(From a letter of the Universal House of Justice to the Bahá'ís of the World, November 1964: Wellspring of Guidance, p. 42)
...as became the case later for Counsellors:
"The members of these Boards of Counsellors will serve for a term, or terms, the length of which will be determined and announced at a later date, and while serving in this capacity will not be eligible for membership on national or local administrative bodies...."
(The Universal House of Justice: Wellspring of Guidance, pp. 141-142)
Perhaps the reasoning for the Guardian still allowing their membership on administrative institutions was due to the still embryonic nature of National Spiritual Assemblies (which were to become the pillars of the Universal House of Justice) at the time when it was not yet possible for them to fulfill the wish of the House that "they be free to devote their entire energies to the vitally important duties conferred upon them in the Holy Writings".
Auxiliary Board members, who are, as with the Hands, also part of the institution of the learned, and who are above the rank (albeit not the authority) of Local Spiritual Assemblies, were also explicitly allowed to serve on a Local Spiritual Assembly if the membership had dropped to nine (i.e., the resources of the Faith were not yet great enough to allow them to take up their protection or propagation duties exclusively):
"As you have stated in your letter, if the membership in a Bahá'í community drops to nine, including the Auxiliary Board member resident there, the Auxiliary Board member may serve temporarily as a member of the Assembly to preserve its Assembly status."
(From a letter of the Universal House of Justice to the National Spiritual Assembly of the United States, March 25, 1966, cited in the compilation, Auxiliary Board Members, in Lights of Guidance, no. 29)