Yes! He participated and won a presidential election.
Evidence to support this are;
1. "On July 1, 1960, Ghana became a republic, and Nkrumah won the presidential election that year." LaVerle Berry (1994). "Ghana, A Country Of Study" Federal Research Division-Library Of Congress-USA, page 33.
2. "In 1960 a plebiscite offered the voters a choice between continuing the system of constitutional monarchy or a republic. In the month of March, 1960 the governments' draft constitutional monarchy were published as a White Paper. The government announced to hold a presidential election for the office of the president simultaneously with the plebiscite, for seeking approval for the draft republican constitution." Tapan Prasad Biswal (1992). "Ghana, Political and Constitutional Developments" Northern Book Centre, New Delhi. page 66.
3. "The published plebiscite results were decisive. The draft constitution was approved by a vote of 1,008,740 to 13,425; in the presidential election, Nkrumah had 1,016,076 to 124,623 for Danquah." William Burnett Harvey (1996). "Law and Social Change in Ghana." Princeton University Press-USA, page 25.
In all these three evidence above, it points out a presidential election which Dr. Kwame won it. In the second evidence above, it stated clearly that "The government announced to hold a presidential election for the office of the president simultaneously with the plebiscite, for seeking approval for the draft republican constitution." This nullifies the claim by Mr. Paul Adom Otchere that Dr. Kwame Nkrumah never participated in a presidential election. He participated in a presidential election and won it in 1960.