Have children update tracking histograms during Get request.
Have children update tracking histograms during Get request.

This won't do a final update of the stats when the
process is exiting but the data isn't so important
that it's worth adding another hook somewhere else.

BUG=546019

Review URL: https://codereview.chromium.org/1874193002

Cr-Commit-Position: 972c6d2dc6dd5efdad1377c0d224e03eb8f276f7@{#386328}

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