qt: Poll ShutdownTimer after init is done
qt: Poll ShutdownTimer after init is done

Summary:
Backport of Core PR12377
https://github.com/bitcoin/bitcoin/pull/12377

Test Plan: `ninja check check-functional`

Reviewers: deadalnix, Fabien, #bitcoin_abc, markblundeberg

Reviewed By: #bitcoin_abc, markblundeberg

Subscribers: teamcity, schancel

Differential Revision: https://reviews.bitcoinabc.org/D2545

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