Is it a standard usage of ‘blue’ to be used as a verb to mean ‘being deflated / become pessimistic’?

That is not actually a verb, but a noun; normally referred to as the blues, it means a feeling of depression or deep unhappiness.

So, it's not that his election "blued", but rather that he had "the (election) blues", but was apparently able to overcome them.

It's not a verb in that use, it's a noun sense which is always plural. "The blues" is a state of melancholy related to the adjective sense you mentioned, and also to "blues" music.

It is often used with a noun adjunct to refer to difficulties with or melancholy about something. Hence "holiday blues" in the well-known song (according to which, there is no cure) and here "election blues" meaning difficulties with an election.

(Edit: incidentally, in the contexts of an election there's yet another sense of blue that's worth pointing out just to avoid confusion - you might say a given constituency "went blue" or "blued" to mean they moved toward a party associated with that colour - generally a centre-right party in Europe, but the in the US it means the Democrats who have been the more left-wing of the two largest parties for quite some time).