Recently, when my son returned from a trip abroad, we used the TV for viewing in family the unsorted bulk of captures he had taken.
The connection between the MacBook and the TV (a 60" Full HD (1920*1080)) was via an AppleTV using Airplay.
While we viewed the captures, he could imediately sort out photos that were doubles or that were no keepers. His aim for taking the photos was to have some memories of his trip, i.e. more touristic than artistic.
As described before, the fact to use the TV was more about being able to comfortably view a large number of touristic style photos as a family, than using it to sort artistic captures.
For that purpose the configuration was fine and allowed to easily identify captures that had flaws or to decide about which of two similar captures was the best. Anyhow, in case of doubt the capture was - in this configuration - also shown in parallel on the MBA screen.
I think that this configuration can also work out for a preselection for more artistic non-professional captures, even so I will prefer my 27" iMac screen. In case of doubt, you might not be as decisive on some captures and keep them for a secound round of sorting on the computerscreen, but for the bulk processing this should work. Considering that you are looking for a 4k UHD screen, this might even better apply.
Also, as mentioned by ScottinPollock, it is more about colour calibration and distance to the screen, if you want to use large TV screens for sorting out captures.