No. While note “names” are rooted in subdividing a meter of 4, note “relationships” (i.e. their value to each other) do not change with meter. A half note and dotted quarter note do not morph into having the same value in different meters, and a half note doesn’t occupy a half measure of 6/8 any more than an eighth note occupies an eighth of a measure.No, that leaves it even more short of filling the required note values. The half cannot equal two "normal" quarters, because the actual 6/8 quarter does that. (See my notation in the prior measure. Also, in 6/8, a dotted quarter fills 3 counts.) I don't think it goes as far as filling the space of two 6/8 quarters- four counts. I've never seen a whole note used in 6/8- nothing larger than a dotted quarter, except for a whole note/rest, which disregards the convention of all the other notes' values and just occupies the entire measure, just as it does in 4/4.
Although the notation here is atypical for 6/8, the 2nd measure does define 6 eighth notes... the half note being the first 4, the next two sixteenths being the 5th and the final eighth being the 6th.
Hopefully this helps clarify things further.