Yes, the most likely answer would be that Mahtan stayed in Aman after the pronunciation of the Doom of Mandos. Mahtan was one of the Noldor, but he did not follow Fëanor (his pupil and son-in-law) to Middle-Earth. Finarfin, who had not joined the revolt of the Noldor either, was King of the remaining Noldor in Aman, and he presumably still rules there.
Mahtan’s daughter, Nerdanel, also chose not to follow her husband Fëanor, and thus avoided the Doom of Mandos as well. So it can be assumed that both Mahtan and his daughter are alive and well in Aman, under the rule of Finarfin.
Sources: (The Silmarillion, ‘The Quenta Silmarillion’)