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Currently this logic needs to be copied and called every time
chrome::AttemptRestart() is called. Moving it within chrome::AttemptRestart()
allows it to be reused. Moreover, it seems that calling
chrome::AttemptRestart() without the said logic (there are such occurrences),
is not correct.

This is in preparation of reducing the number of "Restart" codepaths in MD
Settings.

BUG=617830

Review-Url: https://codereview.chromium.org/2033173002
Cr-Commit-Position: refs/heads/master@{#398195}